A NUMERICAL INVESTIGATION OF TIDAL CURRENT CIRCULATION IN THE GULF OF MAINE by Arthur Paul Drennan United States Naval Postgraduate Schoo THE SI A NUMERICAL INVESTIGATION OF TIDAL CURRENT CIRCULATION IN THE GULF OF MAINE by Arthur Paul Diennan October 1970 TkU document ka& been appAjOvcd ^ox public kz- lecuz and 6atc; /jU dJj>VvibuXA,on u> ujiLLmitzd. T i I*)? A Numerical Investigation of Tidal Current Circulation in the Gulf of Maine by Arthur Paul Drennan Lieutenant, United States Navy B.S., United States Naval Academy, 1964 Submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN OCEANOGRAPHY from the NAVAL POSTGRADUATE SCHOOL October 1970 tLl^ c.i IBRARY kVAL POSTGRADUATE SCHOOE DNTEREY, CALIF. 93940 ABSTRACT The hydr odynamical -numerical model of Walter Hansen is used to compute tidal heights and tidal currents in the Gulf of Maine. The model uses two adjacent open boundaries at which the tides are prescribed at each time step, using four tidal constituents. The grid size is six nautical miles and the time step is thirty-one seconds. Seven data runs are reported; one uses the tides and no wind and the remaining six use uniform wind fields in consort with the tides. A modified method of handling the topographic data is used. The pertinent results of the study are: (l) the use of Hansen's Model with adjacent open boundaries produces broad subjective agreement with observed data, (2) the modified method of handling topographic input data is workable, (3) wind direction and velocity produce slight variations in tidal height, (h) wind direction and velocity modify the direction of the tidal currents considerably and produce some significant increases in tidal current speed, and (5) the modifying influences of wind fields on tidal heights, tidal current velocities, and tidal current directions are more noticeable in shallow water areas than in regions of deep water. TABLE OF CONTENTS I. INTRODUCTION : 13 II. THE EQUATIONS 18 III. THE NUMERICAL MODEL 2k IV. THE INPUT DATA 32 V. RESULTS 38 A. VERIFICATION OF HANSEN'S MODEL 39 B. THE EFFECT OF WIND FIELDS ON TIDAL HEIGHT, TIDAL CURRENT SPEED, AND TIDAL CURRENT DIRECTION h3 VI. CONCLUSIONS 59 VII. SUGGESTIONS FOR FURTHER RESEARCH 63 APPENDIX A 65 APPENDIX B 70 BIBLIOGRAPHY jk INITIAL DISTRIBUTION LIST 75 FORM DD 1^73 77 LIST OF TABLES I. Tidal Constituents 36 II. Water Elevation (cm) after 10 Hours 48 III. Water Elevation (cm) after 2k Hours 49 IV. Waiter P^levation (cm) after 35 Hours 50 V. Maximum Change in Water Elevation (cm) 51 VI. Tidal Current Magnitude (cm/sec) /Direction (°T) after 10 Hours 53 VII. Tidal Current Magnitude (cm/sec) /Direction (°T) after 2k Hours 5^. VIII. Tidal Current Magnitude (cm/sec) /Direction (°T) after 35 Hours 55 IX. Maximum Change in Tidal Current Speed (cm/sec) / Tidal Current Direction (°T) 56 X. Average Current Velocity Due to Wind 57 LIST OF FIGURES 1. Gulf of Maine 16 2. Grid Networks 25 3. Flow Chart 30 k. U. S. Coast and Geodedic Survey 5 Minutes after Low Water at Boston k0 5. Hansen's Model; Low Water at Boston k0 6. U . S . Coast and Geodedic Survey 5 Minutes after High Water at Boston kl 7« Hansen's Model; High Water at Boston h'\ 8. Gulf of Maine; High Water at Boston kh 9. Gulf of Maine; Slack Water at Boston ^5 10. Gulf of Maine; Low Water at Boston h6 8 TABLE OF SYMBOLS AND ABBREVIATIONS x,y space co-ordinates t time u,v components of mean velocity H total depth water elevation in relation to the undisturbed sea surface X,Y external body forces wind stress components g acceleration of gravity f coriolis parameter r coefficient of friction Laplace operator Ah coefficient of horizontal eddy diffusivity density of water N,M horizontal and vertical grid co-ordinates (also n,m) average water elevation u,v average wind velocity components 2 half time step bottom friction hydrostatic pressure proportionality factor between the components of wind stress and the square of the wind velocity a numerical smoothing parameter grid size Hw . ,,. maximum water depth MAX M2,K1,S2,N2 tidal constituents 10 ACKNOWLEDGEMENTS I wish to express my sincere thanks to everyone who has assisted in the preparation of this study. In particular, I expend my gratitude to Mr. Paul Stevens of Fleet Numerical Weather Central for suggesting the study. Next, my thanks to Dr. Taivo Laevastu of the Fleet Numerical Weather Central oceanographic research department for his pro- gramming assistance, encouragement, and helpful suggestions. Finally to Dr. Edward B. Thornton, my thesis advisor, my sincere thanks for his patience, understanding, probing questions, and constructive criticism that contributed greatly to the completion of this project. 1 1 12 I. INTRODUCTION The knowledge of the currents of the ocean, in adjacent and marginal seas, and in estuaries has long been of the utmost importance to navigators and inhabitants of coastal regions. Many attempts have been made to under- stand the currents produced by physical processes such as storm surges, tides, and ocean currents. Years of observations and measurements have resulted in a vastly increased knowledge of the physical processes of the sea. This knowledge has been applied in navigation, coastal engineering, commercial fishing, and in prediction of tides and tidal currents. There is a need for more thorough understanding of the physical processes of the ocean in order to cope with such modern problems as pollution, deep water salvage operations, mining the continental shelf, and farming the sea. The need for this knowledge leads to questions concerning the possibilities of reproducing oceanic motions and how best to accomplish this goal. A successful model for reproducing oceanic motions leads to a capability to predict these motions and hence, hastens the possibility for various groups of people to benefit from the sea. Oceanic motions produced in a numerical model must be compared with actual measurements. If the correlation is reasonably close, then some confidence may be placed in the model. After calibration, the model can be used to forecast with all the practical applications that this 13 implies. Electronic computers make the use of numerical models practical and reasonably economical. Numerical models are flexible in that the boundary conditions and variables involved are easily altered to meet changing needs. Hence, more extensive use is being made of numerical models in predicting physical motions of the sea . The hydr odynamical -thermodynamical equations, in a general form, provide a background for understanding the problems of oceanic motions. These equations form the basis for the model developed by Dr. Walter Hansen at the Institut fur Meereskunde der Universitat Hamburg in 1935. Hansen's model has been used to reproduce physical processes in a number of bays, tidal estuaries, and marginal seas. Examples include the North Sea, Baltic Sea, The English Channel, The Straits of Gibraltar, The Bosphorus, Persian Gulf, Chesapeake Bay, Long Island Sound, Danang Harbor, Tonkin Gulf, and the Gulf of St. Lawrence. Practically speaking, there are a large number of ocean areas where there is a need to determine oceanic physical processes which could be solved by numer ical-hydrodynamic means. The primary purpose of this study is to extend the coverage of the Hansen model to the region of the Gulf of Maine and to verify the model in this region. The determination of the general tidal circulation in this ^k region and the modifying effects of various wind fields on the tides and tidal currents is an objective of major importance. This is true for locations where data for comparison are available as well as for points such as those on the continental shelf and slope where no such data could be obtained. The region of study includes the area between ^0° and 45° North latitude and extends from 66°30' to 71°30' Vest longitude, a total area of 90,000 nautical miles. (Figure l) This primarily oceanic area extends from the southern extremity of the Bay of Fundy near Grand Manan Island off the coast of Maine south to include Cape Cod, Nantucket Shoals, and nearby environs. The bottom topography is irregular in the central Wilkinson Basin region. ( 1 00 fathom contours shown in Figure 1 ) It becomes more regular to the north approaching the Bay of Fundy, to the south in the Nantucket Shoals area, and as the coastline is approached. The underwater landscape is principally continental shelf, but in the lower southeast corner, the continental slope is crossed with an accompanying plunge in water depths from 100 fathoms or less to 1 600 fathoms and deeper. The land-sea border is rugged and frequently indented. This is particularly true along the coast of Maine. The various bays and inlets form an interesting and unusual coastline which includes several unique features. The most dominant feature is that of Cape Cod which extends 15 MAINE 11 Cape Cod <^J7 COOFM FIGURE I Gulf of Maine 16 like a giant fishhook into the sea. The canal across Cape Cod is another unusual feature of the area as the tides and tidal currents at the eastern and western ends of that body make an interesting comparison. Several large islands such as Martha's Vinyard, Nantucket, and Grand Manan are all strategically placed to produce an influence upon oceanic motions that may be of interest. Finally, the large tidal constituents of the Bay of Fundy affect the Gulf of Maine region. The Gulf of Maine is important for several reasons. There are large commercial fishing interests in the area. The port of Boston, Massachusetts, is an important maritime region as is the southern portion of the gulf where sea lanes carry trade between New York City and various world ports. Numerous hazards to maritime safety are attested to by the number of shipwrecks in the area, especially on Nantucket Shoals. There are many other reasons for the region's importance but these are perhaps the most important. 17 II. THE EQUATIONS The classical problem of the tides in the world ocean can be stated: Determine the tides and tidal currents from hydrodynamical equations using the known tide generating forces and the geometry of the sea bottom and coastline. It is then possible to compute the tides and tidal currents quantitatively using the hydrody- namical differential equations without resorting to measurements of these quantities. This problem has been studied since the time of Newton. Mathematicians and physicists such as Laplace, Bermoulli, Poincare, and others, have worked on the tidal problem. The common goal of their combined efforts was to solve the hydrodynamical equations analytically. Solutions were obtained only for geometrically simple oceans. Recently, Pr oudman and Doodson developed a method of computing ocean tides for regions bounded by meridians. In all these efforts, the essential influence of the depth distribution on the tides and tidal currents was considered in a geometrically simple manner. Con- siderable differences have been found to exist between tides and tidal currents in the actual ocean and those computed for geometrically simple oceans. The equations used in Hansen's model are based on the hydrodynamical differential equations derived from the Navier-St okes equation. They are the equations of motion: 18 and the conservation of mass equation: H+^^h)^4chv) = o (3) where x and y are the space co-ordinates; t is the time; u and v are the components of the mean velocity; H is the total depth; Othe water elevation in relation to the un-disturbed surface of the sea; X and Y are the external body forces; | and | are the wind stress components; g the acceleration of gravity; f the coriolis parameter; r the coefficient of friction between water and the sea floor; A the coefficient of horizontal eddy diffusivity; and £j^ the Laplace operator. The eddy diffusivity terms are interpreted as an averaging of the u and v components. Hansen states that the computations are always stable for A, values greater than zero. He also uses an averaging coefficient, a, which is a function of A, and of the local and temporal h step length. (when A =0 , a=l) The tides, being long waves, extend their influence over the depth of the oceans. The equations, as stated, 19 are integrated from the sea floor to the sea surface. This reduces the number of variables and unknown functions by one. The two horizontal components of the averaged velocity over depth remain. Another assumption involved in using these equations is that the pressure is hydrostatic and that the changes in pressure are due solely to changes in surface water elevation. Advection terms are considered to be small and are ignored when using these equations. This has been found to be a good assumption for long wave problems. These assumptions help bring equations (l),(2), and (3) into a more useable form. The problem of the geometry of distribution remains once these assumptions have been made . The motions of the ocean are difficult to solve analytically, especially if the equations are used in their general, non-linear form. Analytical solutions require considerable simplification of the boundary conditions and the equations can only be solved for a basin of regular shape and simple wind distribution. The Gulf of Maine is irregular in shape, non-uniform in depth, and exhibits varied wind patterns. To deal with these problems an implicit method for achieving time dependent solutions to equations (l),(2), and (3) was developed using a finite difference approach. The resulting finite difference approximations are: 20 The overbars indicate averaged terms where the averaged velocity and water elevation components are given by: U On,**) *olH (»\j**) + ~3 £ M. ^n-»,/»n) -f (7) 21 The values of u , v , and in equations (4) - (6) are given by: (10) (11) The half time step is given by 2 p\ The depth in terms of H and H is approximated by: u v ^^ J 13) W^ fa,**) » fo u, fa^)* JjT 7 5 (*\«n)+ J f^^«#)f( and My fo#^)*Kvfa,*W)*^ 5 J fa,**)+jfa,^*fWiZo The external body forces composed of the wind stress and barometric pressure anomoly are computed using the following formulas : 22 and x*« <*"> H <|L<») ±Afs 1 ' w rr7$ (15) (16) The components of wind stress are expressed as: Cx) *\U» t"'« AWX^„%VUy )'* (17) and *f Ctf^ = A Vfy (U/x % VUy*-) ''* (18) The bottom friction is assumed a quadratic function of the velocity. The respective horizontal components are given by: The partial derivatives in equations (l), (2), and (3) are replaced by finite difference approximations. The boundary values are then prescribed as known functions of time. The values of sea level and velocity are determined step by step by the difference equations starting from arbitrary initial values of the same quantities. 23 III. THE NUMERICAL MODEL The model developed by Walter Hansen is based on four major conditions to obtain solutions: (l) that the equations of motion must be in a suitable form, (2) that the driving forces acting on the area of study are given, (3) that boundary and initial value conditions are specified, and (h) that the area of investigation is known in regard to coastal outline and depth distribution. These conditions are met in developing the Gulf of Maine model. The equations used are in the form of the finite difference formulas given in the previous section. The driving forces acting in the area, including the tides at the open boundaries, the coriolis parameter, the direction and velocity of the wind field, the acceleration of gravity, and the coefficient of friction are specified to insure a uniquely determined solution. The open boundaries are specified and the tidal constituents along those boundaries are known. The depth distribution and coastal outline are obtained from U. S. Navy Chart BC 708. The grid network used in the Hansen model is shown at the top of Figure 2. It consists of three separate sets of grid points: (1) the water elevation, or z points, at the grid intersections, (2) the u points located to the right of and midway between successive z points, and (3) the v grid points located vertically beneath and mid-way between successive z points. Each of these points is located by the same (N,M) co-ordinate 24 N VC3,l ) N *ZC3>« + ZC2,4Q/2 X-Z POINT • U POINT OV POINT ri£i irf 2 Grid Networks, 25 designation. The N-axis is perpendicular to the first open boundary and the M-axis is parallel to that same input boundary. This grid set-up requires the preparation of three separate sets of arrays. The first set consists of symbolic data for the z grid points. The z points are coded 0 for land, -1 for a land-sea boundary, and 1 for a point located over the water. The separate u and v data decks are also coded 0 for land and -1 for a land-sea boundary point. The oceanic points in the u and v data cards are coded with the charted depth, in centimeters, at the respective points. The question arose early in this project as to the necessity of using three separate sets of data cards. The land and land-sea boundary areas are largely duplicated in the three data decks. Since both the u and v grid points are located half way between successive z grid points, another question arose as to the possibility of averaging successive z grid points horizontally and vertically and using those values at the u and v points without sacrificing accuracy. Consequently, one set of data cards is used. The z grid points are used, coding 0 for land points, -1 for land-sea boundaries, and charted depth in centimeters for the oceanic points. This alternate grid network is shown at the bottom of Figure 2. The use of only the z grid points for data make 26 several program changes necessary. The modifications consist of computing loops that average the values of successive z points horizontally and vertically to produce values of topography for the u and v points. These changes enter into the program in the initial data handling subroutine. Problems arose using the averaging process in this study to obtain data for the u and v grid points. The effect of averaging a boundary point, coded -1; with either a land point, coded 0; or an oceanic point, coded with charted depth in centimeters; is to produce a boundary point. This creates boundaries that are too wide. The result is that islands become larger than they really are and that narrow, restricted channels are closed. The latter effect is apparent in the Grand Manan Channel at the northeast corner of the area. The first few runs of the program ended with errors as the values for the tidal height in the Grand Manan Channel rose as high as one thousand centimeters. This is above built in program limits and is an unreasonable height for the tide in this area. The process of correcting the boundary points involves additional arithmetic function statements to spot correct the points found to be in error. It is not useful to do any revamping of the z grid points. The u and v points are corrected with direct statements changing those points that require alteration in value. 27 This program requires the changing of one hundred three values at u points and sixty-four of the values at v grid points. These changes enable the program to run to completion. Figure 2 also shows typical boundaries using Hansen's procedure and the revised method. In Hansen's method, at the top of the figure, a step type boundary is shown. This boundary is drawn to the u and v points as it blocks off the coastline. In contrast, the revised method shows a step type boundary that is drawn to the z points to accomplish the same objective. The revised method offers less flexability in adjusting the boundary to the coastline since it can be drawn to only one set of grid points. Hansen's model has been tested in areas with one open boundary, such as Chesapeake Bay, with opposing open boundaries, for the Straits of Gibraltar, and in the "along the coast" problem, for the area from Santa Barbara to San Diego, California. This model for the Gulf of Maine uses two adjacent open boundaries and is an extension of the testing of the model to this new mode . The FORTRAN II program is shown in the flow chart in Figure 3- The main program consists of one program control, five principal subroutines, and three plotting subroutines. The main program control calls the various subroutines when they are needed and stops the program when it is completed. 28 The program starts by reading in all initial data, in subroutine J02 , with the exception of tidal data at the input boundary. This subroutine also computes the value of all compound parameters used in the program and finally, prints out the input data that was read in as a check on the accuracy of these data. This information is stored in plotting subroutine D01. Then subroutine JOk prints the computed horizontal fields of water elevation, current magnitude and current direction at the desired time intervals. These values are then stored in plotting subroutine D02 . Subroutine J05 performs the main computations required in the model. It averages and smoothes the u, v, and z values. It computes the actual u, v, and z values at each step. It calls the wind current sub- routine. The wind current subroutine, S01 , reads in the values of the wind fields. In the integrated equation wind currents are assumed to reach the bottom in shallow beach areas, and to extend downward to the top of the thermocline in regions of deep water. The dotted lines represent a second sequence of printing out the computed values by J04 and the storage of these values for future plotting by subroutine D02 . The program then proceeds to compute the values for the special points in subroutine S08 . The program ends by storing this information in plotting subroutine D03 . 29 READ INITIAL VALUES PLOT STORAGE D03 SO 8 SPECIAL POINTS WIND CURRENTS J02 START ' PLOT STORAGE PRINTOUTS SO MAIN PROGRAM CONTROL --> A >' J04 <- — > DO 2 PLOT STORAGE JOS MAIN COMPUTATIONS FlGURE-l Flow Chart 30 The information from the three plotting subroutines is then stored on a magnetic tape which in turn serves as the input to a separate plotting program. Appendix A contains an identification of the symbols used in this program. 31 IV. THE INPUT DATA The first parameter chosen is the grid size. The size selected depends on the area of study, the detail desired, and the available computer core storage memory. The large area of the Gulf of Maine makes the use of a large array computer, the CDC 6500, necessary. The grid size of six nautical miles used in this study requires 225>000 bytes of core memory to run the entire program. This is over one-half the available memory of the computer A smaller grid size, of say three nautical miles, requires even more memory. Because of rough topography a larger grid size results in a less accurate reproduction of the tides and tidal currents due to over smoothing of the depth distribution. The selection of a grid size fixes the size of the computation array. A six nautical mile grid size used in an area five degrees -of latitude by five degrees of longitude means the computational grid array will be 51 x 51 units. The number of points on each open boundary is fixed by the geography along the boundary. In this region both open boundaries contain only points located over water. Each open boundary then contains 51 points. The selection of the special points ; at which the effects of wind on tidal height, speed, and direction are studied, is based on many factors. The principal reason is the interest value of the point. Any of the 32 approximately 2,000 grid points located over water are suitable for selection. The points chosen for this model are: the open sea outside Boston, Massachusetts, the center of Cape Cod Bay, the center of Buzzards Bay on the western side of the Cape Cod Canal, the river mouth near Portsmouth, New Hampshire, the indented coast near Portland, Maine, the port of Rockland, Maine, Bar Harbor, Maine, the center of the Grand Manan Channel, a point in the center of Wilkinson Basin, the channel between Nantucket and Chappaquidick Islands, a point seaward of Cape Cod , a point over the continental slope, two points in the region of Nantucket Shoals, and finally a point south of Grand Manan Island over the continental shelf. These points are shown in Figures 8, 9> and 10. Each type of topography, water depth, and coastal location is represented by one of these special points. The objective is to describe the region by comparison and contrast at the various special locations. 2 The acceleration of gravity is 980.665 cm/sec for this problem. This is a widely accepted value for gravity . The program provides two parameters for computing the wind effects on the tides and tidal currents from a given barometric pressure distribution. These parameters are the coefficient of geostrophic wind, 0.65> and the -3 3 average air density given by 1.1 627 x 10 gm/cm . These parameters do not enter into the program when uniform 33 wind fields are used. This model uses uniform wind fields . The program provides the option of using four separate tidal constituents at each open boundary or of using only the velocity of the M2 tide at these same boundaries. This model uses four separate tidal constituents at each open boundary. The coriolis parameter used is given as 9*5620 x 10 sec . This is an average for the latitude of the region. The coefficient of bottom friction, the proportionality factor between the wind stress and square of the wind velocity, and the smoothing parameter used with the coefficient of horizontal eddy diffusivity are given by values which Hansen found to be the most suitable after much experimentation with the model for widely separate bodies of water. The coefficient of friction used in this study is 0.003. This as a dimensionless parameter. The components of the wind stress and the square of the wind velocity are related by the proportionality factor 3.2 x 10 . The numerical smoothing parameter, a, is 0.998. Hansen obtained the most accurate results with his model using these values. The one-half space step is determined by the grid 5 size. In this problem it is given as 5*5506 x 10 centimeters, or three nautical miles. The maximum length of the time step is determined from the maximum grid size 3^ and depth in the area according to the Courant-Friedrich- Levy criterion. . • 8A 4l = -, i// (20) In this formula, t is the time in seconds, 9 the grid size in centimeters, g the acceleration of gravity, and H the maximum depth in the area of computation in max centimeters. When this criterion is applied to the Gulf of Maine, a time step of 31 seconds results. The wind field characteristics are determined by the programmer . The wind fields are specified by the wind velocity in m/sec, the wind direction computation co-ordinates, and the time, in seconds, when the wind starts blowing. The wind fields constitute one of the two primary inputs to the program. Their values are introduced at each grid point for every time step throughout the program. The tidal constituents are obtained from tabulated values for various locations throughout the world. The M2 , K1 , S2 , and N2 constituents for Grand Manan Island are used for the eastern open boundary and the M2 , K1 , S2, and N2 constituents for the western end of the Cape Cod Canal are used for the southern open boundary. These values are introduced at each respective open boundary point for every time step throughout the program Table I summarizes the values of the tidal constituents used . 35 TABLE I Grand Marian Island W. Cape Cod Canal Constituent Speed Direction Speed Direction (cm/sec) °T (cm/sec) T M2 251.5 339 50.0 230 S2 39.0 015 10.0 275 K1 13.7 131 10-° °80 N2 ^9.^ 312 15.0 205 The final data decisions are those concerning how many runs to make and the various time considerations involved with each run. A total of seven separate runs are reported in this thesis. The first is a run using only the tidal inputs and no wind. This run requires a total of approximately five hours of computer time on the CDC 65OO to accomplish thirty-five hours of computations This is sufficient to cover almost three semi-diurnal tidal cycles and to establish the tidal circulation. The next four data runs use 20 knot wind fields from the four cardinal directions. In each case the wind is introduced at the five hour mark and terminated at thirty-five hours. Output from the model is obtained at two hour intervals. The objective is to combine the wind and tidal circulation and see how the wind fields modify the tides and tidal currents. The final two data runs use the same format for length of computation, introduction of the wind, and 36 termination of the wind. The velocity is increased to 30 knots and the directions are altered from the southeast and northeast respectively. The input parameters and their data card format and arrangement are contained in Appendix B 37 V. RESULTS The results of this study consist of a computer out- put for each of the seven data runs. Each computer print- out contains the water elevation in centimeters, the resultant tidal current speed in centimeters per second, and the tidal current direction in degrees true for each grid point at two hour intervals. Each run contains nineteen such printouts. The same information is printed out for each of the fifteen special points. This produces a great deal of data. Each two hourly printout of values contains computed information for nearly two thousand oceanic grid points. It is difficult to interpret all of this information without some reasonably detailed plots. The ideal situation is to develope a computer program to plot part or all of the data manually in some suitable format. Because of difficulty with the plot program and time limitations the alternative of plotting part of the data is necessary. The results are discussed in two sections. The first section concerns the verification of the Hansen model in the Gulf of Maine. The second section discusses the effects of various wind speeds and directions on the tidal water level, tidal current speed, and the tidal current direction. 38 A. VERIFICATION OF THE HANSEN MODEL The verification of the model requires that some observed data be compared with the numerical values obtained from the model. The observed data used in this instance is tidal current data compiled by the U . S. Coast and Geodedic Survey. This data represents current measurements extracted from light ship observations over a period of several years. The currents are not correlated with the winds present at the times that they were measured. This means that the comparison of data that follows actually compares average currents produced over a period of years by widely varying atmospheric conditions with the instantaneous values produced by the model for a unique set of prevailing conditions. Figure k presents tidal current speed in knots and tidal current direction as indicated by the vectors, for the observed Coast and Geodedic Survey data. This description pertains to the time of five minutes after low water at Boston, Massachusetts. Immediately beneath this data, Figure 5 presents the same information obtained from the model for the same approximate locations and time of low water at Boston, Massachusetts. In extracting comparison information from the model, the closest grid point to the location of the observed data is used. The measurements are not compared at exactly the same geographic location. Figures 6 and 7 perform the same respective functions for the high tide situation. 39 ko FIGURE 6. co/ast and 6eodedic Survey Data 5 Minutes J&sPZ* 0.3 /AFTER High j/2^^ Water at \ *? *Jfl AT1 Boston | / <^o °IJ i'/t ° to <\7\ >l»0 9 £J 41 Comparison of these figures shows broad subjective agreement between the observed data and that computed by Hansen's model for the high and low tide situations. The agreement shown is general and not in detail. In fact, there are specific points at high and at low tide where disagreement is evident. The tidal speeds do show an order of magnitude agreement. The directions of the tidal currents appear reasonable for both high and low tide. The agreement shown suggests that currents in the region are probably tidally dominated. The information used in Figures 5 and 7 is obtained from the no wind run of the model. The reference station used is Boston, Massachusetts to conform with the Coast and Geodedic Survey data. The region of comparison is known as George's Bank and covers an area bounded by latitude 40°30'N and ^2°N and between 67°30'¥ and 70°W longitude. This represents only a portion of the entire Gulf of Maine area. The meteorological conditions prevailing in the Gulf of Maine vary considerably from month to month. There is a noticeable difference in the pattern of the mean wind flow between winter and summer. In February, a month typical of the winter regime, the mean winds are westerly with a velocity ranging from 7 "to 27 knots. The summer season, represented by August, has mean winds that are predominant by southerly to southeasterly with velocities from 3 to 16 knots. The Gulf of Maine is a 42 region of cyclonic storm activity and exhibits a wide range of wind speeds and directions during any given period . The verification if somewhat disappointing in that many questions remain unresolved. The principal obstacle remains ascertaining the conditions prevailing when the observed data was recorded by the Coast and Geodedic Survey. Unfortunately, the data does not provide the meteorological conditions prevailing at the time the measurements were made. Since they are averages obtained over many years it is assumed that many separate wind fields prevailed during these current measurements. This appears to preclude a more accurate verification without additional specific information. Figure 8 presents the tidal current circulation in the Gulf of Maine when high tide occurs at Boston, Massachusetts. Figures 9 and 10 show the same information for slack water and low tide respectively. Slack water and a zero tide level occur almost simultaneously for this location. All three diagrams are compiled from the no wind data run and show tidal circulation not driven by any specific wind. B. THE EFFECT OF WIND FIELDS ON TIDAL HEIGHT, TIDAL CURRENT SPEED AND TIDAL CURRENT DIRECTION The effect of the various wind fields on the tides and tidal current circulation is presented in a series of k3 FI6URF 8 GUUF OF M/uNe (D BOSTON, MASS- (3 CASHES LEDGE HM«BflP E* CAFE COD CANAL © CHAPPAQUIDICK IS. NEW BEDF0RD>MASSo © PROW NCETOWN, MASS. PORTSMOUTH/NoHo ©CONTINENTAL SLOFS # NANTUCKET SHOALS $) GREAT SOUTH SHOALS d$ SEAWARD OF 6RAND MANAN ISLAND PORTLAND, ME* ROCK LAND, MS". BAR HARBOR.MEo GRAND MMAN IS, -» <50 — » 50-100 Scale Ccm/sec) -* IOO-I50 » I50-2O0 * 200-250 — * >250 44 FIGURE 9 SULE QFMAfNE bL^f^f&? ©boston, mas so ® cashes ledge (d eto cape cod canal © chappaquidick is. ©new {3edford,masso 0d pr0vincetown,mass© 6) portsmouth/n. h. 200-250 50-100 > I50-20O > >250 ^5 '" ' ' ' ]" ' T ' " . " | , i _+_ LJ-Taj. L 1 B/aIL * bOQa*^ v '0 ^G£g gX ! | •AAAA "'^~^N-* i t--* + l -^^ ^' -_L .zf ~ u "aST^S v _, i - III 1 tC -vC. 1 ?0t5^ VJ7 S ^> ^■^Nl \ <14- ■■■■■■■I t i > fc.AA.j«.- ' 1 , ; / „ w » f^i L-^ i_i LA,- -4^—4- I 1 ; ... pcxb . j^i i '■■ - =t — %— Xi "7 y L>S^ !«Jl / * tJtfan r^i 1 ^t 4 ^*1 VOi 1 1 IF _i » 1 /''• «"J 1 L 1 J.. \ 1 1 > 1 \ 1 ! ! ^ / 1 j i5i / M H pOOfl 1 I / 11 1 i L 1 il -SlT *^7- _,%»"*■ -*#t-" t t • • r I i — T' * "* t I J J ? 'fl5 H^vii pi u/ |4 ^ f*)\ \*i d J mm i ^T -t±4- 4-^ £tlt vl i 1 t j II t f 1 2S§A 1 r •' * .gagsrpnr. -rr-~ - - III T fL \ wn \!> i ! i 1 ± 41 _ it + toy j Wji ^ . H j.j_i._i_jL .. . ^ pog ! /L i it^^f- ' ' 1 ■» / -.1 -iffO M |/4 ! b 1 ! i / "2 "KHLi ififi ' '* -4-44- - ' x ! ' ± ' 4»- 1 f ! I S 1 ! rx^ J*". ? i : it 4: tji ' ± "I ^ u 1 i r\ i -±\ •* \ *■ . ^_4 1 , *1 *l-4 1 1 1 t — — - * C ... ^rU Vi? ! « /7>vi I i 4-. mr4,, f--i- « i i r ' K-^'.r _^ * ! ' ' 1 ! ' l> ! 1 ill Adx /v?N i ' i ill 1 :jr:p_4~ip -2p - 1 ;|i u ^ 1 1 1 111 1*1^ f * 4> ^ j * i 1 ! ^if 1 1 1 ! 1 1 i 1 i 1 a J T ! 1 I'1 j^j | jfc 1 i — ----- - -[ - -L--± sj j * 1 I 1 r j • i" k^ 1 i 1 >iz-*z±±:izz^rV --v -> -+ y-t--»--;. » \ }ru ,| | •CV'i A & ,i,J^*T. -71 i 7011-1-1 I * >3 ! ! I 68 1 ' 1 ! 67 : "TO w^m FIGURE 10 Gulf ofm ©BOSTON, MASS. ©CASHES LEDGE (g> Eo CAPE COD CANAL © CMAPPAQUIDICK IS* INEW BEDFORUMASS. © PROVINCEToWN^MASSo &PORTSMOUTH/N.K. ©CONTINENTAL SLOPE 5 PORTLAND ) ME. 250 k6 tables. The values used are those computed for the fifteen special points for each of the seven data runs. The duration of the wind is considered by choosing times such that the fully arisen sea and non-fully arisen sea cases are considered. The wind is introduced at the five hour point in each data run. The first time chosen is at 10 hours or five hours after the wind starts. Five hours is not sufficient time for a twenty or thirty knot wind to build into a fully arisen sea (i.e. time for the energy content of the sea to be saturated). The second selected time is at 2.h hours or 19 hours after the onset of the wind. This time frame is sufficient for the 20 knot winds to generate a fully arisen sea but not for the 30 knot winds to accomplish the same result. The final time selected is at 35 hours or 30 hours after the onset of the wind. This allows the 30 knot winds to generate a fully arisen sea and explores the effects of allowing the wind to blow over an already fully arisen sea for eleven hours in the case of the 20 knot wind fields. The water elevation after 10 hours, (5 hours of wind) is summarized for the fifteen special points in Table II. Similar information for 24 hours and for 35 hours of wind is contained in Tables III and IV respectively. Table V contains the maximum change in water height produced by any wind field at each point for times ten, twenty-four, and thirty-five hours. The range of maximum wind produced changes runs from no change at New Bedford, Massachusetts hi H H W •J m < Eh ON CM c c^ o ■" ■• ' — ' en m O NO c^ CM r— r— ^f o Eni MO !> c\ e~ o^ o m CM c- ON NO o ON T— O H ^^ r— o c ip o> 00 jt O c c^ 00 NO l> en c^ Q j 1 MD 00 1 ? 00 cm 1 r— ■ 00 1 NO I 00 1 IP o h 1 i i 1 1 • 1 1 1 cn^ 1 eg en O a -H/ £ »" O o X IP in t> NO 00 OH CM -3- CM no i> en CM o -d- NO r- T— 00 ON £;s . J 13 i m j- o NO CM n r- O o> , IP m ON NO NO O i On ooj CM 00 NO 00 in o &j 1 I l 1 I 1 i 1 1 T— nu] i ' g I on CM c 00 IP oo ON O CM, o CM -3- NO NO CM en lO CM en NO r~ o CM in m cm NO 00 * — CO O §3 oo i 00 {> 1 T— 00 NO IP o o « i l 1 i | i 1 i r— w CM £j 1 i H ^ p 2-S -3" .* O en -tf ON 00 O o r^. {> NO !> NO o En !2i H r- t~ CM -3- 00 O NO CM o -cf CM en -tf n £h Cn e^ O CVi NO m CM O o O in m NO T- NO < 1 MD 00 i ON 00 CM r— 00 NO 00 in _ CM Ci 1 i 1 ; 1 1 i i 1 1 7! S3 j 1 o 1 ■ — ■ e-1 e en vo O r— m NO ON o NO 00 o *> 00 CM -=H O 2 ON ON CM ON CP o CM CM 00 en in r~ T— o fe ^ H o 2 £ en 1— O IP 00 o NO O I> CNJ c- -=f en o in H IT 1 I> 1 oo l> r- 00 NO 00 in En o . 1 1 i 1 1 i i i 1 H < > CM £ L ._ j . ! l! I ! _ J en o o CM NO H o o 00 ^ ON ON NO NO OO W EH c o g On • • CM ip e~ o ,_ CM CM ON CN c^ I> -tf ON K £ H NO -tf C NO o -tf 00 O r^- en r- -d- J" ON Jt w 2 ^ . ^ oo 1 00 r^ T— 00 NO £v m ^ 1 1 i i 1 1 1 " 1 ,— I < o « I 1 1 i > > CM 01 1 ! : 1 1 1 00 -H/ c NO CM -d- o o -d- NC | CO ON . 00 CM 00 ^t CM CM C^ e~ CM CM m C^ -=*■ C^- r^ O o 5 13 H »n o" c NO 1 ^ r^- O {^ t- CM -d" e^ I o- in > i IP i 00 I • i 1 \ — 1 00 1 NO 1 i in H i! T 1 i c/ i 1 | w ,_ J U" j a \ C/] Ph C/l < ' S C/" I « • H o J c > fc. X • C/3 S J < X , 2 4 I W H M en o w e H j c/) ft 5 : Cr CJ P4 cv \o o T— c^ o o J- ,_ • i ] 1 en m 1 1 ON c^- r— T— cv r- cn -* o w i i 1 i 1 1 1 i 1 i r~ c^ 52, 1 1 1 t J CM o cv cv 1 1 r^: o o cn en o On m cv' {> o ^ o r^ cv -d- o o m cv r- On C^ -* OS 00 52 H • « 5* ° T— o cv r— T— 1 m| o NO o m m o °! o J en in 1 On| I> cv T— cv T— % -=f O Erl i i i I i | 1 1 1 i 1 T— -3- 00! On; o T— in cv oo -d-! m VO K O 55 i> cv1 cv o\ -3- -tf T— ! cv 00 -d- \o On m; - t> 52 H • . • • • • l • < • • • • • . • -cr « 3 o T— o r^ 00 o -3" 1 o cv -d- J-' CV ON' On J> cv 1 O - 1 1 en i 1 00 i ! i i CV 1 CV 1 m cv o «~ cv cv On m -3- 1— o C^ -* H 55 H < 3 5*1 ,— o o r— c\ r— cv o VO T— NO m cn T— o i en J- 1 On C^- T— T— cv T— r> -3- o • i 1 1 1 1 1 i 1 i t— js cv W 1 o ■^ .^ 1 53 Eh P VO o 00 en en On o {> On On en oo cv CV o o 55 m J> cv cv m c^ vo cv 00 cv T— o in m cv; H £ H H W 5s CM o o VD -3- cv r- o m cv VO -d- cv o On < i 1 CM -* 1 00 r^ 1 T — cv T— cn cn > O • 1 i i i | ! 1 1 1 i T— a cv 53 i 1 j . CO HH ! no cv o ■ o 1 X H 0 en en cv -cf m T— en cv 00 T— en 1> ON cv On| w O 52 • • • oo l>- -d- NO . ON J- On o CV e^ On1 Eh 55 H T o o • • • • o • • • • • • •! < W 5s i cv cv o 00 en J- -3- -d; On CN oo: 5s 1 o • CM CO cv 1 -3- i 1 00 i 1 1 CV 1 1 1 » ■ ■ 1 CV 1 H i t -tf -3- o {> o -3- -d- o o r^- o i e^ i 00 lO i cv: CV CV cv en o o cv cv On oo m O m ON > r~ o g o o o j- en ,- 00 o -=f T — m J" ,- ON J 0\ 52 H 1 1 cv -=r 1 00 I> 1 T — cv i — CV en 5s 1 i 1 I 1 i ! i i 1 T — 1 • 1 CO • • CO w J J CO CO CO ' X CO < ; w; CO • • H < o J o 52: < X 1 • CO s J < X 52 X • w H M CO o l CO .H - 55 1 * • X. W o 52 _^ •T1 1— t . CO < p i a w 52 o H ^ J CO F O ! 55 CO pq X W 2 5S X < p P o < Eh o < o H o 52 w H ^ Eh Eh ' 52 52 1 H s P fa D p P pq ! < J P w 52 W O < H \ o p O 52 55 X X a o H w CO 52 Eh Eh < J CO K 5s K X O ~> < CO < O 52 52 W « o < W O o o < X < X X O < Pi Pi j m 1 ° 52 Cm I * X pq O o o Pm o i fc O O ^9 > H W pq < Eh HP1 00 c o J J 1 j r- 1 ol r-. c- CO o -3"! -3- c o 53 r e> c\ in , R ui \0' CMi -H; V0 CM 00 CM, 00 c 53 R < • 1 . J • .1 J . P M r i f" c O CM id «-i i SO -5f Ol NO 1 J> c*- c^ 1 CNj NC o « 1 il 1 1 i en p ^ Hd r_ o c 00 CVI r-i «- O: i — -H; 00 00 J f^ ir O 53 o n c\ -d- H no inj CM CM CM CM 00 ° CN IT 2 H 1 .1 i • i • • • • • • 1 i , p ^ c\j n o IT 1 , CM o r> °i c~ c* NO c^ J> r> • -cr o J 1 1 CMj l] i -3- 1 1 1 c- i ■ 1 ! i CO! 1 1 j i CO I 1 « 1 ! t i P H Q <- o o O NO o NO' o r IT NO -H- en 0. -d 010^ n CM I> -H"( n CN CM 00| o o 00 vo c^ e^ S ^H • . • • ., J • 1 • • • • • . • p > o o. *r* 1 t-j vol O A r^ NO NO CM IT , en in 1 1 T— | en ^t 1 en J> en o * CM 52 ' 1 j i 1 W S r i t H 1 I 1 H h p ^ m o -H- 00 r^ cm! o MD m t^- _^- ^r m id o g ir 00 cm _3" r>j CM {>■ CM T— -d- J> m -d- c oc P 53 H . < 2 52 o T— o -* o O -H; O -d- NO NO -d- CM "1 r- CM -H/ ^t 1 1 en r-- o • 1 1 > i i s c\i p , o 1 53 Eh P a CM o t — ON J- c\ o 00 ^ rs r^- ■ o o o O 53 r^ 00 CM IT | o NO en CM c\ NO m NO 00 CM in H S3 H ■ « « ; ^ H P 52 o o o o c^ O o O n NO m o -* < >! o • W! cm £ i • 1 I 1 -H; 1 1 en 1 ■ J | i i 1 W 1 i E- P «: O 53 c- en o en no On O O NO IN r- T— -H; C H P 52 o ON CM !> 0\ r> o CM o\ VO r- 1 ^ IT \ < CM o o {> rH o r— o NO m -H/ 1> \ 52 o • CM CO 1 1 -H/ 1 -Hr I 1 en 1 — - ■ {^ i ! -H/ o o i 1 CM cn 00 NO o ON r- cn o -H; C r^ P o 00 CM O O ^f C^ CM ON 00 in, f^- J" •^f o O 53 . S3 H o O OS o o o CM o NO m CM m 52 1 i 7 j -3- 1 -3- 1 i en • • • CO P i w p p CO | CO CO P CO < w CO ! 5i i • H < o P c s^ < 1 • CO S p < i-r Sz X W H P CO o r. < 1 |H • j £ , 52 P C I 53*" ~ t CO < p j. w p „ 53 O H 5s P CO c > CO p 1 « , 5r ! J2 52 P O 53 P H H (r^ ^ ►— 5? O p p t— i P P pq < P D P 53 p c < H - o p C > 53 53 p 5S O ° P 5^ CO £ E- o p 52 : < < < CO 53 53 i o < < pq cr I p ! P P P p P H H p E- 52 o CO £• E- « H W 53 1 p P > Eh ^ < o p 52 « o p < CO < O 53 53 C£ ' J c I < W c 1 o o < P < K rv O < PC PC 1 ° 53 pj p 1 p | PQ O o O P O 53 i Ol c 50 TABLE V LOCATION MAXIMUM CHANGE IN WATER ELEVATION ( CM ) 10 HOURS 24 HOURS 35 HOURS BOSTON, MASS. 7.57 5.65 4.35 CAPE COD BAY 2.72 1 .96 2.50 NEW BEDFORD, MASS. 0.00 0.00 0.00 PORTSMOUTH,N.H. 10.38 13.53 1 1 .48 PORTLAND, ME. 13.39 9-97 9-35 ROCKLAND, ME. 2.69 2.92 2.00 BAR HARBOR, ME. 7.35 7.33 6.75 GRAND MANAN IS. 0.00 0.00 0.00 CASHES LEDGE 5.82 4.70 3.44 CHAPPAQUIDICK IS. 17.72 18.46 7.52 PROVINCETOWN,MASS . 5.95 2.51 0.75 CONTINENTAL SLOPE 1 .53 1 .76 1 .90 NANTUCKET SHOALS 5.38 5.44 4.63 GREAT SOUTH SHOALS 3.36 4.08 2.56 GR. MANAN CHANNEL — 2.08 2.27 1 .93 51 and Grand Manan Island to a change of 18.46 centimeters for Chappaquidick Island at the 2k hour time. The greatest change in tidal height due to any wind field amounts to 18.46 centimeters or approximately one half a foot for the locations and conditions specified in this study. In computing the differences reported in Table V, the no wind data from Tables II, III, and IV serves as the base or reference data. No attempt is made to identify the wind field responsible for producing the greatest change at each point . The changes at deep water locations are small while the greatest changes in tidal height induced by the wind occur at points in relatively shallow water . This may be a consequence of the averaging of the model equations over depth. The lack of any change at New Bedford, Massachusetts is attributed to the effects of geography. This location is sheltered by boundary points from every wind field used in this study. The maximum changes observed do not necessarily occur when the wind has been blowing for its full duration. The effects of the various wind fields on the tidal current speed and direction at the special points are presented in Tables VI, VII, and VIII for the ten, twenty- four, and thirty-five hour times. A summary of the maximum changes in these quantities is presented in Table IX. Once again only the greatest changes are considered 52 H > W PQ < P I i Eh Q cJ X J ^ 1 en T— ^— o\ ^o {> J- CM i NO NC O § cm; CM CM m en T— CM 0\ -cf o CM O H NO NC CO fe H d cn o en O! o O ON O o cn cn o: o c tt 3 a "V \ \J v. \ \ \ \ \ ^ ^N ^s f) « o m T- en rs J> o J" o NO j> cn r> r- O i o w oo1 NO -d- X 5 en t> lO NO -3" CM J- c^ r- K j cn 2j i T— T— ,— o ' J p d CM o> J- NO X -d- ON J- o o m CM T~ en w O 5^ CM1 -tf C^ O cn r^ CM ON m -3- cn o CM X ^■ s ^ t-l c o o o O o O On o o en en T- o c p-1 H M 3 \j \ \J \ ^ \. \; \ \ \ ^ V \. Eh 4 on o r^- CM l> cn O -* NO r— m c~ ifi o u -d-' J- r^ X Jt ■* X m c> CM CM m X r>- P cn 73 ,— i — ,— NC *— '! J3 H C\i ^i r— o °l T— O CN o T— en en *- o c 1 p s "N \J \ N "S N \ \ \ ~N \ . ^. CM m X c> o I> CM o X X o r^ NO T— NC olo « r- CM Cf CM ^ MD -d- r r~ en ^ o o H | CM J3! H I T— T— r— P 1 ! ed i p r iri IN o ON \0 r^ ^t ON ^_ j- - X NO ,_ a, HI 02i -* -d" r^ in r- CM ON m c- c CNi o ON r> NO P 5^ M cn en o n c O ON o cn cn O o o \ W 3 \ \ \ \ "x \ \ \ \ \ \ \ n. On o r— no c^- vo o en X o ON CM o i> O O H -d- j- m t^ CM » m IT- cn ?l m X r^ w cm a *- T— CO o 1 , J" in 0, ON -d" cn X ON r- §a cm CM X in en in CM ON -3" n a t— O NO NO \ en o en o T— O ON o o en en * — c O p 2 ^ \ s £ \ \ \ \ \ \ \ ■ \- i T— X o -d- X r^ o T— On en X CM VO R o J ■n -=r CM NO CM VO m CM en e^, en r~ f- P CM JZ '- '" r~ H S3 o , h P o S3 CM en -* X o\ VO t- ON -* r^ X -cr CM j- o 2 §g n CM O o en en CM ON m NO CM T— ^~ r^- l> o o T— o o T— O ON o o cn en »— o £h \ \ \ m en \ \ \ \ ■\ i \^ *s £ o « n - r™ ■ m CM - o T— OJ m en NO c N p o CM CO CM N NO NO en T — r— m 10 T — en m i X ^ On NO CM en X -tf ^o ON X NO en CM 0^ J p c* en o o e^> c- CM ON m ir^ i CM rr- i— f^ t ^o < Q O 123 cn en «- o o r— o ON o o cn en T— o o S2 H \ \ \ m N. \ ^\ \ \ \ 1 \| V| H H i— CM -d- o o\ o r— T— en cn X 1 NO NO Eh cn en 1 * NO en CM \o m J" CM t — C^\ -=f r> j {^ • * • CO P CO p J CO CO CO P CO < r~^ CO • • H < o p 1 2 a < X • CO X p < 1 X • c^ H W CO c X S3 • [h 2 • • SS w o £ HZ ^q o CO < Q W a fc o H ! > p CO H H CO m P X X X K ! < p P O < : 1 p J p P p < CO A ^ K Pi c K -^ CO <; o S3 S3 p i o < H O o o < rv < W i « O 1 < — H ^ m o Z Oh Ph K pq o o o p O 1 2; u q 53 H H > pq <; Eh ^ 00 On cn m r^- m ON 1 CN! T" T — ON 1 mi -d- 1 1 -d- o S CM {> T— -=t O o p NO ■* -=r r^- T— n NO m m CM T— m ^ X -3- en ^ i *" r— ,— 1 | ^ 9 r>- -Hz ; tri C\i , CM m CO ON; CM T— 00 VO m m On W o 3 55 H no O ' rJ T— | J" !> CM On' NO cn cn {> cn cn m £ 0 T— 0 O O O O ON O 0 cn CM T— r— 0 H K £j N \ S N \] \ \ \ \ \ \ \ \ H « CM O ol 00 On o\ J" ■ O. T— m t- £> -d- -d" CM o p -H; J" vo ^0 T- C^ t^- m NO On T— -d- J- NO Eh cn 7i 1 1 T— T™ ■ < I I 1 TT EH 9 r^ O T- ^t- r^ NO On NO -ct- O H ON ON VO o O 55 ON Os On c^ m t>. 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MANAN CHANNEL 1/4 2/3 3/5 56 and no attempt is made to identify the particular combination of wind speed and direction that causes the greatest change at a given location for a given time. The variation in tidal current speed runs from a high of 60 cm/sec at Boston, Massachusetts at 2b hours to a low value of only 1 cm/sec in the Grand Manan Channel at the 10 hour point. Thus the range of changes varies from 1/50 of a knot to 1 .2 knots in speed. The variation in the direction of the tidal currents due to the addition of the winds is great. The range is from a very small change of only 2 degrees to an almost complete reversal of direction of 178 degrees. TABLE X WIND VELOCITY (KNOTS ) 10 20 30 40 50 AVERAGE CURRENT VELOCITY DUE TO WIND AT FOLLOWING LIGHT- SHIP STATIONS BOSTON AND BARNEGAT 0.1 0.1 0.2 0.3 0.3 r DIAMOND SHOAL ( CAPE HATTERAS ) 0.5 0.6 0.7 0.8 1.0 ALL OTHER LOCATIONS 0.2 0.3 O.k 0.5 0.6 Tivdal current tables published by the U. S. Coast and Geodedic Survey discuss the effect of the wind on tidal current velocity. Table X shows the reported observed . differences caused by various wind speeds. These data are based on observations made by lightships during a period of 5^ years. They do not consider the duration of 51 the wind field and this helps explain the differences between the data reported in Table IX and the observed values shown in this table. Points located over deep water, such as the Cashes Ledge point, exhibit very little change in tidal current speed or direction due to the effects of wind. The largest response of these quantities to different wind fields is found at points located in shallow water areas. Geographic position again enters into the evaluation of these factors. The largest changes in speed and direction of the tidal currents occur at points near the boundary between the land and sea. Such points as Cape Cod Bay, New Bedford, Massachusetts, Rockland, Maine, and Chappaquidick Island all exhibit large deviations in the direction of the tidal current in response to various wind fields. The use of equations integrated over depth spreads out the effect of changes at deep water locations over the full depth at those points. All equal amount of change at a point in more shallow water is distributed over a lesser depth. This helps explain the greater changes noted in shallow water locations. The model also considers that there is no net mass transport perpendicular to the shoreline. This introduces the explanation that tidal currents flowing at the surface are offset by a subsurface or bottom flow in the opposite direction, so that the net mean current as presented by this model is zero. 58 VI. CONCLUSIONS The conclusions reported in this study are divided into three major categories. The first concerns the use of Hansen's model in a mode with two adjacent open boundaries and a modified method for handling the topographic input data. The next category is the verification of the data produced by Hansen's model with observed data. The final category concerns the effects of wind fields on the tidal heights, tidal speeds, and tidal current directions in the Gulf of Maine. The use of Hansen's model with two adjacent open boundaries produces reasonable results for the Gulf of Maine region. The modified grid network used in this study requires minor adjustments in its use but is workable and results in less time and effort expended in coding and key punching topographic data. Hansen's model may be used in a variety of ways. The fact that the use of the model with adjacent open boundaries produces reasonable results does not mean that these are the best answers possible. The model can be used with one open boundary, various parameters are subject to change, and any combination of wind speed and direction is possible. The verification of the Hansen model reported in this study is only in broad subjective agreement with observed data. The verification is for a given set of conditions which can be altered to produce an entirely different result. 59 It is sufficient to say that using the Hansen model with adjacent open boundaries produces reasonable results which are in general agreement with some observed data for the Gulf of Maine. The conclusions concerning the effects of various wind fields on tidal height, tidal current speed, and tidal current direction are limited in scope and are necessarily confined to the fifteen special points used in the study. Any attempt to extend these conclusions to the other points in the Gulf of Maine is unwarranted as each point must be looked at individually. The effect of the wind fields used in this study on the tidal height at the points in question is slight with the largest change being only one half a foot. The greatest changes are found at points located in shallow water. In contrast the smallest changes are found for points located in deep water. Geographic location appears to be important in considering the effect of wind fields on the height of the tides. The effect of the wind fields on tidal current velocity at the specified locations used in this thesis varies considerably. The wind speed and direction is found to have less effect at deep water locations than it does at shallow water points. This is expected because the equations used in this study are integrated over depth and hence, the effects of the wind are spread out over a large area in deep water, vice a much smaller area in 60 shallow water. Physically this is a reasonable result. The speed of the tidal current increased by 1 1 00$> amounting to 1.2 knots at Boston, Massachusetts for the greatest change recorded. This may be of significance and indicates that the wind speed and direction does influence tidal current speed. The effect of wind speed and direction on the resulting direction of the tidal currents is pronounced. The variation is again found to be greater for points located in shallow water than for deep water locations. In some cases, the direction of the tidal current is found to almost completely reverse under the influence of a wind field. This indicates that wind speed and direction can not be ignored in the prediction of tidal current direction. It is important to realize that the current experienced by an observer at a given point is a summation 'of the tidal current, wind driven current and any major oceanic current, such as the Gulf Stream, at that point. This study concerns itself entirely with tidal currents and the effects of various wind fields acting on them. The Hansen model provides a reasonably fast, generally accurate method of predicting tidal current speed and direction, and tidal height for any given uniquely specified conditions. In this regard, there is a great need for data with which to verify the model. Current measurements should be combined with the atmospheric conditions pre- vailing at the time they are made to enable investigators 61 to steady the complete atmospheric oceanic system of interactions. It appears the model is most useful for storm surge prediction. This is vital information for coastal engineers and residents of coastal areas. The model is capable of producing information for any point specified and hence can assist in filling the void of knowledge for areas where no observed data on tidal height, speed, or direction is recorded. This project represents only one attempt to study the tides and tidal currents in the Gulf of Maine. As such it only begins to explore a most complex and involved s ub j e c t . 62 VII. SUGGESTIONS FOR FUTURE RESEARCH The Hansen model is capable of many separate modes of operation. Use of the model in the Gulf of Maine region should be continued and the model should be used in as many different modes of operation as feasible in order to find by comparison and contrast that combination of boundary conditions and parameter values that yields the most realistic results for the region. The modified grid data handling method requires verification. The Hansen model should be run again for the Gulf of Maine with the same parameters using the original method of handling the topographic data. A comparison of results between the two methods should help determine the worth of the modified method of handling these data. The rugged, fractured topography of the area suggests that a grid size of six nautical miles may be too course. A grid size of three or maybe even two nautical miles may be necessary to bring out more accurate results for the tidal height, tidal current speeds, and tidal current directions in this area. The smaller grid size should eliminate any effects of over smoothing of the depth distribution possibly caused by the six nautical mile grid size. This may require the sub-division of the Gulf of Maine into two or more smaller regions in order to reduce the computer time involved in such efforts. 63 The investigation of the effects of various wind fields on the tidal heights and tidal currents is worthy of further efforts. This is essentially storm surge prediction and it is of practical interest to mariners, coastal engineers, and many other groups of persons. It could, some day, prevent property damage or even loss of life by adequately predicting the effects of a severe s torm . Constant experimentation with the Hansen model is the only way to discover whether it is in fact valid for all types of water regions. It's use should be extended to as many separate oceanic areas as feasible. The Hansen model used in this study is limited in the sense that it does not accurately portray the density distribution of the ocean. The recent development and testing of a so-called multi-layer model should help overcome this difficulty. The results of the multi- layer model and this single density Hansen model can someday be compared to determine which most accurately describes the tides and tidal currents in the Gulf of Maine. It may be that for some regions the single density model is sufficiently accurate. In contrast, the multi- layer models may offer significant improvements in the accuracy of reproducing the tides and tidal currents. Much remains to be accomplished before mother nature is duplicated by a deck of computer cards. 6h APPENDIX A ABBREVIATIONS AND PARAMETERS USED IN THE PROGRAM M N z(n,m) u(n,m) V ( N , M ) RAD ( N , M ) ANG ( N , M ) QU(N,M) qv(n,m) rest(n,m) dir(n,m) zm(n,m) . zst(n,m) htz(n,m) htu(n,m) HTV ( N , M ) hgu(n,m) HGV ( N , M ) xk(n,m) yk(n,m) A(I) grid index (parallel to entrance) grid index (perpendicular to entrance) water elevation ( CM ) U-component of velocity (CM/SEC) V-component of velocity (CM/SEC) resultant current speed (CM/SEC) angle from geographic north of resultant current speed fields for summation of the U and V components of currents for computation of the rest currents see QU(N,M) average speed of rest current (CM/SEC) direction of rest current (geographic co- ordinates ) used in J05 as a smoothing intermediate used in J05 as an averaging intermediate water depth at the water elevation (z) points water depth at the U-points water depth at the V-points actual water depth at the U-points (lIGU=HTV + Z) actual water depth at the V-points (lIGV=HTV+Z) U-component of the wind current divided by depth V-component of the wind current divided by depth characteristics of the wind field 65 A(1) A(2) A(3) NU(l) MU( ;i) NZ( I) MZ< I) NK( I) MK( ;i) NA( [i) MA{ ;i) zi ( i) Z2| [i) U1 ( i) U2( ;i) Z3( ;i) z4< [i) U3I [i) vh\ [i) V1 I [i) V2 [i) V3 [i) time when the wind starts (SEC) wind speed (m/SEC) wind direction (computation co-ordinates) wind field delimeters (N and M co-ordinates of the upper and lower right corners of the wind field) see NU(l) co-ordinates (N,M) of the points used as selected special points see NZ(l) co-ordinates (N,M) of the points on the first open boundary see NK(l) co-ordinates (N,M) of the points on the second open boundary see NA(l) amplitudes of four tidal constituents at the first open boundary (CM) see Z1 (i) see Z1 (i) see Z1 (i) amplitudes of four tidal constituents at the second open boundary ( CM ) see Z3(l) see Z3(l) see Z3(l) names of special points water elevation at special points (CM) speed of the current at the special points (CM/SEC) 66 v4(i) AFGN F G SIGMA ALPHA R ROL RBETA C DL . DT T T1 T2 NE ME TE KKE KO IZE NG IUE TW TIC LEN direction of the current at the special points arbitrary problem number coriolis parameter ( 1 /SEC ) o acceleration of gravity (CM/SEC ) angular velocity of the M2 tide (RADIANS/SEC ) smoothing parameter friction coefficient air density (GM/CM-3) coefficient of geostrophic wind drag coefficient \ step in space (CM) \ step in time (SEC) time (SEC) interval between printouts ( SEC ) field output counter (SEC) field size delimeters see NE end time of computation (SEC) number of wind fields the number of points on the open boundary minus one number of open boundary points (first open boundary) number of points on second open boundary twice the number of wind fields time when the wind starts counter see TIC 67 POC BETA A1 A2 A3 Ak A5 C1 C3 si NURU NURV JA NE1I MEH NEHH MEHH WERTO WERTU WERTL WERTR WERTOL WERTOR VERTUL WERTUR see TIC (1 -ALPHA )/k 2DT F(A1) R(A1) DT/DL G(A4) 0 if no wind, 1 for wind C (A (2 ) )x( 1 0 , 000 is a unit conversion factor which converts (M/SEC) to (CM/SEC) after A(2) is squared time when wind stops number of special points printout line counter indicator, if 0 set U=V = Z = 0, if/:0 read initial values NE-1 ME-1 NE-2 ME-2 storage location for U and V during smoothing and averaging see WERTO see WERTO see WERTO see WERTO see WERTO see WERTO see WERTO 68 WURZEL SQRT(ZM2-ZST2) GRZ A3 ( WURZEL) 69 APPENDIX B INPUT PARAMETERS AND THEIR FORMATS The Data Input Cards Card 1 Format 2*+I3 J A , NE , ME , I ZE , IUE , KKE , NURU , NG JA indicator, JA=0, Z = U = V = 0; JA=1 read initial values o NE,ME field size delimeters (51 ,51 ) IZE number of points at first open boundary (50) IUE double the number of wind fields (2) KKE number of wind field characteristics (3) NURU number of special points (15) NG number of points at the second open boundary (50) Card 2 Format 9F8 . 3 A FGN , G , ALPHA , RBETA , C 1 AFGN problem number (7001 ) G acceleration of gravity (978CM/SEC2) ALPHA smoothing parameter (0.998) RBETA coefficient of geostropic wind (O.65) C1 wind indicator; 0=no wind, 1 =wind Card 3 Format 9F8 . 0 DT,TE,T¥,T1 ,T2,SI,T,T3 DT \ time step (15 SECS ) TE length of computation ( 126000 SECS ) TV time when wind starts (18000 SECS) T1 interval between printouts (7200 SECS ) 70 Card 3 (cont . ) T2 field output counter (0 if outputs are desired from the start of the problem; otherwise any other delayed starting time, e.g. 7200 SECS) SI time when the wind stops (126000 SECS ) T time (initialized at zero) T3 time when plots are desired (every 7200 SECS ) Card h Format 6E12.4 DL , F , SIGMA , R , R0L , C DL half the grid size ( CM ) _ r F coriolis parameter (8.55 x 10 ) SIGMA angular velocity of the M2 tide (1.4088 x 1 0" ) R friction coefficient (0.003) ROL density of the air ( 1 . 1 627 x 10"^) C drag coefficient (3.2 x 10~ ) Card 5 Format 2*+I3 N coordinate of special points M coordinate of special points Format 24l3 N coordinate of points on first open boundary M coordinate of points on first open boundary Format 2^13 NU,MU NU N coordinate of wind field delimeter 71 NZ, MZ NZ MZ Card 6 NK, MK NK MK Card 7 Card 7 (cont. ) MU M coordinate of wind field delimeter Card 8 Format 2^13 NA,MA NA N coordinates of points on second open boundary MA M coordinates of points on second open b oundary Card 9 Format 10A5 V(I) V(l) names of selected special points Card 10 Format 9F8 . 2 A(I) A(l) time when the wind starts (18000 SECS ) A(2) wind speed (M/SEC ) A(3) wind direction (in degrees in computation coordinates ) Card 1 1 Format 1 2F6 . 0 HTZ HTZ depth cards (usually more than 10 cards; 217 in this program) Card 12 Format 9F8.3 Z 1 ,Z2,U1 ,U2 Z1 amplitude of first component (CM) Z2 amplitude of second component (CM) U1 amplitude of third component (CM) U2 amplitude of fourth component (CM) 72 Car d 13 Z3, Zk ,U3. M Z3 Zk U3 vk Format 9F8 . 3 amplitude of first component ( CM ) amplitude of second component (CM) amplitude of third component (CM) amplitude of fourth component ( CM ) 73 BIBLIOGRAPHY 1 . Hansen, W. , The Reproduction of the Motion in the Sea by Means of Hydr odynamical -Numer ical Methods, p. 3~54 > Mit teilungen des Institutes fur Meereskunde, 1 966. 2 . Fleet Numerical Weather Central Technical Memorandum Number 2 1 , Hydrodynamical Numerical Models of the Oceans Present and l-utute, by Professor Dr. Walter Hansen, p. 1-11, May 1969- 3. Fleet Numerical Weather Central Technical Memorandum Number 27, Tides and Tidal Currents in the Strait of Gibraltar Computed with the Hydrodynamical Numerical Model of W. Hansen, by T. Laevastu and P. Stevens, p. 4-13, March 1970. 4. Fleet Numerical Weather Central Technical Note 51 » Applications of Numer ical -Hydr odynamical Models in Ocean Analys is/ For ecas ting , by T. Laevastu and P. Stevens, p. 1 -4p , July 1 969- 5 . Tidal Current Tables 1969 Atlantic Coast of North Amer ica , p. 184-188, U. S. Department of Commerce, 1969. 6 . Coastal Currents Along the Atlantic Coast of the Un ited States, p. 1-26 and Figures, U. S. Depart- ment of Commerce, 1942. 74 INITIAL DISTRIBUTION LIST No. Copies 1. Defense Documentation Center 2 Cameron Station Alexandria, Virginia 2231^ 2. Library, Code 0212 2 Naval Postgraduate School Monterey, California 939^0 3. Department of Oceanography 3 Naval Postgraduate School Monterey, California 939^0 k. Dr. Taivo Laevastu 1 Fleet Numerical Weather Facility Monterey, California 939^0 5. Dr. Edward B. Thornton 1 Department of Oceanography Naval Postgraduate School Monterey, California 939^0 6. LT Arthur P. Drennan 1 Hudgins Post Office Mathews, Virginia 23076 75 76 Security Classification DOCUMENT CONTROL DATA -R&D iSecurity classitication ol title, bodv ol abstract and indexing annotation must be entered when the overall report is classified) 1 Originating activity ( Corpora le author) Naval Postgraduate School Monterey, California 939^0 2a. REPORT SECURITY CLASSIFICATIOr TTnr lassifiprl 26. GROUP 3 REPOR T TITLE A Numerical Investigation of Tidal Current Circulation in the Gulf of Maine 4 DESCRIPTIVE NOTES (Type ol report and, mc I us i ve dates) M^stPTi's Thesis: October 1Q?0 * S «uTMORiSi (Fifslnt/ne, middle initial, last name) Arthur P. Drennan 6 REPOR T D A TE October 1^70 7a. TOTAL NO. OF PAGES 73 7b. NO. OF REFS 6 Ra. CONTRACT OR GRANT NO. 6. PROJEC T NO 9a. ORIGINATOR'S REPORT NUM8ERIS) 96. OTHER REPORT NOIS] (Any other numbers that may be aa si gned this report) 10 DISTRIBUTION STATEMENT This document has been approved for public release and sale; its distribution is unlimited. II SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Naval Postgraduate School Monterey, California 939^0 13. ABSTRACT The hydr odynamical -numer ical model of Walter Hansen is used to compute tidal heights and tidal currents in the Gulf of Maine. The model uses two adjacent open boundaries at which the tides are prescribed at each time step, using four tidal constituents. The grid size is six nautical miles and the time step is thirty-one sec- onds. Seven data runs are reported; one uses the tides and no wind and the remaining six use uniform wind fields in consort with the tides. A modified method of handling the topographic data is used. The pertinent results of the study are: (l) the use of Hansen's Model with adjacent open boundaries produces broad subjective agreement with observed data, (2) the modified method of handling topographic input data is workable, (3) wind direction and velocity produce slight variations in tidal height, (k) wind direction and velocity modify the direction of the tidal currents considerably and produce some significant increases in tidal current speed, and (5) the modifying influences of wind fields on tidal heights, tidal current velocities, and tidal current directions are more noticeable in shallow water areas than in regions of deep water . DD FORM I NOV 6 5 S/N 0101 -807-681 1 1473 (PAGE n 77 Security Classification A-3140S Security Classification key wo ROS Hansen's Model hydrodynamical-nuraerical Gulf of Maine tidal current topographic DD,Frv"..1473 < S/N 0101-807-682 1 BACK 78 Security Classification A- 31 409 stri* 23«* 52 \%Zl^ Thesis nves ti _ nau . y jnve^ * "un* V.Mai cur- ga' in Dreonao , reunion 23*5! XeVuU of »»- 9SCP^4 Thesis D7365 c.l 122135 Drennan A numerical investi- gation of tidal cur- rent ci rculation in the Gulf of Maine. thes07365 AS,Z!'Ca] ,nvest|9at'on of tidal curre 3 2768 002 00675 1 DUDLEY KNOX LIBRARY