fe Lae INTERNAL TIDES OFF SOUTHERN CALIFORNIA Analysis of data obtained hy NEL thermistor chain W. Krauss. ° Research and Development Report U. S. NAVY ELECTRONICS LABORATORY, SAN DIEGO, CALIFORNIA (=P) co es — c= = «z 1353S ROS | Lad = 68E1 LYOdIu/ TIN 6 July 66 DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED HANNA O 0301 0040537 4 PROBLEM Investigate and report on the nature of internal waves in the sea. Specifically, study the differences between spectra of internal waves as obtained from an anchor station and those measured by a towed thermistor chain, and apply the results to internal tides in the sea off southern California. RESULTS 1. A method accounting for doppler-shift effects was used to interpret data recorded from San Diego to Hawaii by moving thermistors. The results lead to a reasonable picture of the internal tides in that area of the Pacific Ocean. 2. It is shown that internal waves can be produced directly by the tide- generating forces. Free diurnal internal waves vanish at 30°N. 3. Internal tidal waves are an important component in the spectra at tidal frequencies in the sea off southern California. It is likely that they travel in a northeasterly direction. RECOMMENDATIONS 1. Verify the theory of internal waves of tidal period with additional measurements with the thermistor chain. 2. Fora complete analysis of the various modes of internal waves, ex- tend measurement of the thermal structure to the sea floor. 3. Supplement the study of internal waves by the use of current meters and salinometers mounted on the chain or at anchored stations; use the data produced to increase the usefulness of thermistor-chain data in the study of the ocean structure (sound-velocity structure) controlled by non- periodic motion such as advection. ADMINISTRATIVE INFORMATION Work was performed under SR 104 03 01, Task 0580 (NEL L40461). The report covers work from August 1963 to February 1964 and was approved for publication 6 July 1966. Financial arrangements for travel and salary were furnished by ONR and administered by Scripps Institution of Oceanography. The author is grateful for the assistance of E. Good, J. R. Olson, D. L. Jackson, C. L. Barker, and P. G. Hansen in collecting data; of Mrs. R. P. Brown and R. F. Arenz in programming and computer analysis; of R. McKinley, J. Larson, and Mrs. A. Moore in computations and plotting; and of O. S. Lee, G. H. Curl, and E. C. LaFond, who reviewed the manuscript. CONTENTS LIST OF SYMBOLS . . . Page 5 INTRODUCTION . ..7 ANALYSIS OF FIXED AND TOWED OBSERVATIONS OF INTERNAL WAVES... 8 NATURE OF FORCED AND FREE INTERNAL TIDES IN THE OCEAN ... 21 ANALYSIS OF CHAIN DATA RECORDED AT DRIFT STATION. . . 28 ANALYSIS OF CHAIN DATA FROM SAN DIEGO TO HAWAII. . . 38 DISCUSSION OF RESULTS. . . 40 CONCLUSIONS. . .52 RECOMMENDATIONS . . . 52 BIBLIOGRAPHY. . . 52 TABLES il Hydrographic Data for Station 1 . . . Page 29 2 Hydrographic Data for Stations 2 and 3... 31 3 Hydrographic Data for Station 4... 34 4 Amplitudes of Fluctuations with Diurnal and Semidiurnal Periods at Station 4... 35 5 Contributions of First Four Modes to the Observed Fluctuations with Diurnal Periods at Station 4... 36 6 Stationary Depth Change of Isotherms in Upper 230 Meters... 40 ILLUSTRATIONS 1 Cruise pattern AB, BA, CD, and DC... . Page 13 2 Graphical presentation of cases (a), (b), and (c).. . 14 11 12-21 ILLUSTRATIONS (continued) Schematic diagram of observed amplitude distribution at an anchor station... 16 Schematic diagram of observed amplitude distribution, from observations made with moving thermistors. .. 18 Mean amplitude spectrum for upper 180 meters, Drift Stations IL, Bo Binel Bo 4 5 BO) Predicted tides at San Diego, California, 10-17 Oct 63... 31 Eigenfunctions W,,(z) for Drift Stations Zrandisienere oz Eigenfunctions at Anchor Station 4... 35 Amplitude spectra recorded by chain towed in cross-shaped pattern. . . 37, 38 San Diego-Hawaii cruise map, showing details of tides. . . 39 Mean amplitudes A. for upper 200 meters, computed from chain records, San Diego-Hawaii, 4-17 August 1961... 41 LIST OF SYMBOLS w(x,y,z,t) Ware): @ Ae b,?) 1/2_ yms amplitude of the Fourier components Fourier amplitudes Amplitudes of the modes, Wo). of an internal wave w/kK, phase velocity Coriolis parameter = 20 sin ® where ( is the angular frequency of the earth and @® is the latitude Acceleration of gravity Bottom depth Horizontal component, used as an index Amplitude of the inhomogeneous term responsible for the development of internal tides (magnitude 10728 em! see73) Fourier components of kg Amplitude of the tide-generation force Integers in Fourier expansions P/p Pressure Salinity Temperature Ship’s velocity (u,v,w) = velocity vector wix,y,z) exp (iat) = wlz)Glx,y) exp (iat) = w(z)G(x)G(y) exp (i@t) vertical velocity Modes of the eigenfunctions, describing the vertical depen- dency of an internal wave with the vertical velocity w(x,y,z,t) T(z) ‘Qo Right-handed rectangular coordinate system, z pointing downward Angle between the ship’s direction and the direction of wave travel de pu ede Delta function Eigenvalue w/a = amplitude of the displacement Potential temperature Wave number in x, y direction Wavelength Weighting factor in the eigenfunction expansion for unequally spaced data A transformation (see equation 76) Density Mean density distribution p U(S,T,p = 0)] - 10° Period Doppler-shifted period A transformation (see equation 79) Phase of a wave, gravitational potential or geographical latitude A wave function of (x,y,z,t) Space-dependent part of the wave function 20 aS angular frequency INTRODUCTION It was shown by A. Defant* in 1950 that internal tides strongly influence the hydrographic situation in the area off California. Since then, various measurements were made of internal waves in this area,” * but the studies did not produce details of the modes of these internal tides, nor of their origin and direction of progress in the open sea. Studies of near-coast areas*’® showed that no constant phase lag exists between surface tides and internal tides. In 1963, Summers and Emery’ cohducted a multiple-ship study in the area off southern California, and on the basis of their measurements formulated a very reasonable picture of the semidiurnal tidal waves in that area. However, their values for phase velocity are not in complete agreement with the values derived from the theory of internal waves. For instance, their recorded component of the phase velocity is about 9 knots in deep water and 0.6 knot over the shallow shelf — values corresponding to about 4.6 meters/sec and 0.31 meter/sec. A reasonable value for the first mode, according to hydrody- namic theory, would be 1.6 meters/sec for the semidiurnal wave. The reason for this discrepancy seems to be that Summers and Emery disre- garded the diurnal internal tides, which play an important role in their records, as can be seen immediately in those from the R.V. Velero IV and USS EXCEL. The study to be reported here was undertaken to gain a broader understanding of internal tides — their natural movements, and the effects of doppler shift upon the direction of their propagation. The areas studied included various points off southern California and a long section from San Diego to the Hawaiian Islands. The data were obtained by use of the NEL thermistor chain,* a towed instrument which records nearly continuous temperature data from the surface to a depth of about 230 meters. The measurements are re- corded in analog form as depths of isotherms. Depending on the informa- tion sought, the towing ship followed an X-pattern, drifted, or lay at anchor. The following sections will present: (1) development of equations necessary for the analysis of the doppler shift of internal waves, (2) development of an equation expressing the nature of free and forced in- ternal tides in the open sea, (3) analysis of the chain data collected from towed, anchor, and drifting stations off southern California, and (4) anal- ysis of the chain data in a long section from San Diego to the Hawaiian Islands. ‘Superscript numbers identify references listed at end of report. ANALYSIS OF FIXED AND TOWED OBSERVATIONS OF INTERNAL WAVES Importance of the Phase Velocity Any small perturbation in an inviscid, incompressible area of the ocean, where currents can be neglected, is determined by the equation 9 a2w ry 2 aw (2 aw a fle d3w 9 ow 0 GH i a PR NE BB are TN ae ap eae = with the boundary conditions w=Oatz=0 (2) and OH OH w=u— + v— where z = H(x,y) (3) Ox oy Equation 1 follows from hydrodynamic equations, the continuity equation, and the incompressibility condition. Surface waves are excluded. In the following sections we restrict ourselves to water areas of constant depth: H(x,y) = H = constant. Expanding w into a Fourier series, w(x,y,zZ,t) -» Py es (z) exp [i (KpX +1) V+ ot) ) (4) k,2,m we get for the vertical dependency Ws en (Y dW dW gh -w?2 aoe Dar Hees - 2 (242) W= 0 zi Z Or W= Oat z= Oandz=H (5) where the indices have been dropped. 5 Long waves are characterized by gl’ >> w*. Furthermore, long waves can be assumed to be long-crested. If they travel in the x direction, we then have x? >> and equation 5 reduces to d2W dW — +1 —+TeW= 0 dz2 dz W= Qat z= OQ and z=H (6) with the eigenvalues Ae K acne (7) = fe € The vertical dependency of the observed fluctuations in the ocean are then described by Cs) Wiz) = » A.W, (2) (8) n=1 The phase velocity of these waves, c, is given by e 1/2 @ 6 C, =— 5 (9) as de | yl = \ 03 if f2<<@, equation 9 reduces to 1/2 eos (=) (10) n € Therefore, the phase velocity can be computed simply by measuring the mean density p(z) and computing the eigenvalues e,, from (6). I‘(z) is generally computed from the formula 1 1 2) oO (z + Az) — a, (2) (11) 1410730, Az Analysis of Data from Anchor Stations Knowledge of the internal wave structure of an area is best obtained at anchor stations, where doppler shifting will not affect the frequencies and where observations can extend to the bottom. The thermistor chain is ideally suited for observations from an anchored ship in shallow water because its temperature sensors are equally spaced. Equal spacing of transducers is essential because description of observations by internal waves requires 10 H N i [i - » vate W (z)dz = (0) ioe 7 = Np Pocadly (12) 0 pall from which, for numerical calculations, N » [oe 2 » ate Wi(2)) Nel, = 10) for)r = 1,2, suNinen(cls) Az; n=1 follows. This equation reduced to (19) only in the case where Az, = constant. If this is not valid, the weighting factors, Az;, influence the result consider- ably. Let q be the number of depths for which the amplitudes, a(z;), have been determined. For depth range a(z,) is supposed to be representative. The whole column is divided into (q+1) subranges and instead of using Az, in equation 13 we can use, after multiplication by g+1/H the dimensionless weighting factors Az (23,1, -2;-)) (GD i i+ SE Gan 2H 1; (14) The weighting factors are 1 for equally spaced Az; , that is for oa) Hea Gal eee 2 Many computations have shown that disregarding the weighting factors (14) leads to erroneous results and further study is recommended. Following is a summary of the formulas needed for processing data taken from records at an anchor station. These will permit comparison of spectra from an anchor station and those from towed instruments. Suppose we have observed the temperature fluctuation, T (¢;, 2,), at an anchor station at the levels z;. From the mean temperature distribution, T(z), it follows that the displacement of the particles from their mean position is given by T(t,, 2;) Zi eis ern abs (15) U 1 oy (dT /dz); From Fourier analysis we find the amplitudes, a and b, for a distinct frequency, wt C(t, 2 ;) = a(2;) cos wt+b(z;) sin at (16) In order to interpret these fluctuations as internal waves we assume W=a; then N N a(z;) = De A Giz.) >. AW,,(2;) (17) where A A, =—, AW a= AM To find the amplitude A, , we use the method of least squares. If the depths, TU? 2; are equally spaced, | N 2 > a(z,)— y AW, z,) = Minimum (18) 1 = 1 i Il must hold; this yields the system of equations N | S a(z,) — » AW (2;) W (2) =(0), HOP 7= IjoaaolN! (19) t=1 n= l from which the A, are determined by using a computer. Equations for b(z;) and B,, have a form similar to equations 17 and 19 and are therefore not shown here. Equations 6 and 10 are used to find the phase velocities and equation 19 is used to compute amplitude of the modes. The study of modes of internal waves from anchor stations in shallow water is greatly facilitated when the observations extend to the bottom. This basic insight into the internal wave structure of an area is generally obtained by anchor stations because the re- cords contain no doppler- shifted frequencies. Doppler Shifts of a Single Internal Wave Using a Moving Sensor We assume that there is only one internal wave present with the period r. If the ship is anchored at x=x,, it can easily measure this period 7. Case 1: Suppose the ship travels with the speed U in the +x direction, and the wave moves with the velocity c, in the direction —x. Then we have a doppler shift and observe the apparent period 7’, given by 11 12 (20) where U = ship’s velocity. With increasing ship velocity, U, the apparent period gets shorter. So A 4 HA ‘>7 for UZ c, andc, >0 (21) Case 2: If the wave travels in the same direction, +x, as the ship, then we have T= (22) U Cy with mS r’S for U Sc, andc, >0 (23) With U>c, _ We again have Case 1 because the phase velocity of the wave is negative relative to the ship’s velocity. Generally, in Case 2, we find 0 S7’S «for UZ c, and c, > 0 (24) Case 3: If the wave travels with the velocity, c, in any direction which makes an angle, a, with the ship’s direction, then the effective ship’s velocity is Usrp = U cos a (25) and we generally write, for the period 7: : : a _ Ucosa (26) Cc with 0 <7r’Sm for 0 Sal 2z It is seen from equation 26 that with a=90° we get ;’=7 as in the case of an anchor station. Equation 26 shows that with no prior knowledge of the direction of progress of the wave there is no possibility to filter the record because the period 7 may appear at any value 7% In (26) the unknowns are 7 and a. The velocity, U, of the ship is known and phase velocity of an internal wave at any period is given by its eigenvalue. 7’ is recorded. In order to determine 7 and a we have to carry out the cruise pattern as shown in figure 1. We define the angle ays U 1 ued < Figure ]. Cruise pattern AB, BA, CD, DC. U and c are known; therefore, ay is also known. Consider cases (a) , — (b) , and (c) , as follows: U < (a) If cos a=+ 1 then 7 U T= 1 == COS a holds. From the legs AB, BA, CD, and DC ‘in figure 1 we have , F , > Up aN Bia PAB Nos 1— cos a 1+—=cos a ¥ T pe T 7™DC CD = 1-—= sing 1+—= sing From these formulas we get : 27'AB 7 BA 27cp 7DC wee 5 7 , 7 (27) "aABt7 BA ep r’ DE 14 and sin g =-- CT Ne = ¢ ED C {7 ~aB-7BA (98) ‘tsa aer Se a 4 \\ fp) 75 © pe The ranges for a are shown in figure 2. c/U Figure 2. Graphical presentation of the cases (a), (b), and (c). U eee ieee pee meaty i If | COS @ > 1 holds, we have to distinguish two possibilities depending ona J z (b) If Ue it and . OSas §, c we have : =" GCOS a— 1 and with ay < w/4 the result is na a 7 if (Nz) Tad a U 2 DC : | cos a—l +uUsin a $1 Cc where the upper sign holds for ag >7/4 and a>n/2-ag ; the lower one holds for ay >7/4 and a the lower sign valid for ag>7/4 and a > 37 eG OL CO) > nl and a arbitrary. The period again is given by equation 29, substituting rpc by tcp. the angle is determined by ais a Ay need a [S C : sing = —— (= ——— 5, cosia— i(1+ = ) (31) l ep U\ 7'aB Doppler Shifts for an Infinite Number of Modes of an Internal Wave with a Period 7 So far one internal wave with the period 7 and phase velocity c has been considered. A case will now be considered where there is again only one period 7 q but the wave is composed of different modes as is the case for all real internal waves. Case 1: If the process is observed at the anchor station, we record the fluctuations N Qn In F(z, t) = } AD We (z2)\cos——t + Baws (2)i sin it (32) n 1 Z, non 7 n=l 0 0 16 where N N tee Je , (2) = > BMW ip are the observed amplitudes of the cosine and sine components. The amplitude and phase spectra are given by Alo, z) = ({s A, Wie (2) +3 B, Wa (z)| ) for O=Og n 0 elsewhere (33) Ee arctan = alr lah Zo a2) M@,z) = ZAW, (z) for @ = ®g not defined elsewhere where A(q,z) is the amplitude density and should not be confused with Br A schematic of the amplitude A(w,z) is given in figure 3. A a x A, A. A SPECTRUM AT AN ARBITRARY LEVEL z. —— > PERIOD 0 | B. VERTICAL DISTRI- BUTION OF THE AMPLITUDE : ( Figure 3. Schematic diagram of an observed amplitude distribution A_W,(z) at an anchor station (eqn. 32). Amplitude and phase spectra are quite different in Case 2 where an internal wave of many modes but of a single frequency, 9) is observed by using transducers that are in motion. Case 2: Because of the different phase velocity c,, of each mode we get the periods “Oni roan (34) 7 if ais the same for all c,,. The process is recorded as N ; 2 2m Ps ty) = » AW. (2) COS == th 13, WW, (@) siin = (35) n=l "O.n 70,n This record is much more complicated because a complete set of apparent periods, 7 0, n for n=1,2,3,...N, is recorded instead of one period that would be recorded at a fixed point. Amplitude and phase spectra are given by 3 1/2 Lye he Di (4,2 a B,) W,, (2) for w= @ Osa TS A tas g oh) = O,n 0 elsewhere (36) arctan — for OOo not defined elsewhere Wwiltlare— less INE Figure 4 shows the same schematic amplitude spectrum as in figure 3 with N=4, using a towed sensor. Because of towing, the internal wave of the period 7) is decomposed into the different modes which now occur at dif- ferent apparent frequencies @, ,, It may be mentioned that the integral over the entire @ range of equation 33 is different from the integral of the entire @ range in equation 36. Case 3: Several internal waves are considered with periods 7,, which travel in the directions a,,, each one composed of a sum of different orders n. Since the ship is moving, the apparent periods 7,, , are given by Cs Zila Ran aleseas. | (37) Alvi AMPLITUDE FACTORS 7 N —<=— iG Figure 4. Schematic diagram of an observed amplitude distribution (AA + Bie) V2 from observations made with moving thermistors. The process is recorded as M N Be he F (z, t) = ' ay We (2) GS t = m=0 n,m . 27 + Be ll (z) sin x t and as long as all Ti m are different, i 2 Bev al A (w%, 2) Ayom © Bn, m W,, (2) for @°= @ n,m = @, = 0 elsewhere arctan OP) =@)5 ¢ (wm 4 z) = n, m not defined elsewhere (38) (40) Now each period 7,, produces a whole set of spikes similar to those shown in figure 4. In general, several apparent periods may coincide. For two internal waves with different periods 7,, and r,,, each one composed of eigen- functions of the order n and n*, apparent periods are coincident, i.e., ™n, m Te m? if 1 —— cos a, T Ch Th =-—_——_ : U (41) ™ |1—— cos a,* Cn is fulfilled. In this case we find instead of (38) and (39), ({s An ll, (De) 3 We ) , n,m n,m A (@%4 Zz) = fOr NG _ ae 0 elsewhere ar so n,m SS nom Bn,m Wn (2) (42) arctan [So oS Sa dbla4 z) = n,m Jan, aa ip (z) Oe ary =a) cet not defined elsewhere Again the apparent spectrum A(w ,z) reflects separation into the different modes similar to the case given by equation 33. Amplitudes of the modes are not given directly. The method of least squares is used for computation of 1a\ 4s and B 1 TP All these considerations have dealt only with one section, for example section AB, of figure 1. The main problem is to find the apparent periods pane 7 ae be in the spectra for the different legs which belong together. Whether this is possible or not depends on the form of the true spectrum. A peak in the true spectrum will occur as an identical peak but at a different apparent period in each of the spectra from two different legs. These peaks must be identified in order to use equations 27, 28, and 30 for 7 anda. Until now, records have been available only from rather complicated areas. In this case we have not been able to identify peaks of different legs. The same could be shown for the power spectrum, P(@,z), instead of the amplitude spectra. Consider a real situation, given by N I? (2,6) = Ss [ A,W,, (2) cos opt + BW, (z) sin wot | n=l N us » [CW (z) cos (ot - a, (z))| (43) n=] The chain, even in this simple case, gives a complicated pattern: 19 20 N i? (eb) = » [A.W (z)cos ,, t+ BW, (2)sin w * t n=l N = » [C,W,, (2) cos(ot — ap, (2))] (44) n=] with 2 Z 27 i 7 OS a Onee DT 0) U (45) 0 n,0 h ——cos a The power spectra for infinitely long series of the type given in equations 43 and 44 are, respectively N PA P (o,2) n> Ge We a) [ Ho-o) + dw + oo)| (46) sll N P(a%z) 21/4 Se Ws (21)? | do-o,, +d/e ss o,/| (47) m= il In reality (see equation 46) , the energy of the internal waves is equal to the square of the sum of the mode amplitudes. The power spectrum of a thermistor chain record leads, however, to the sum of the square of the amplitudes of each mode. The total energy obtained by integration over the whole range is, accord- ing to equation 46, given by 2, LP ekepnl (2) = v2 » C,, Wr 2] 68) el Equation 47 yields, however, N c 2 2 2 lO) = 1/2 DS Go Wee (a) (49) ia Il and therefore fl (50 P sota'2) * Protar@? That is, the total energy or variance recorded with the thermistor chain is different from the actual variance or energy in the ocean. Example: If ae Woz) = sin: C,,=(-D7n then at z=H/2 we get r 2 Pn. i= 1/2 lim » (DE 1a ain we VW AG endl vote noo In P totay = 1/2 lim » 1/n? sin? (n7/2) = 1/2 7?/8 n>oo nN In this case, the energy with the chain is twice the actual energy. Choosing (—1)" for n £5 0 for n >5 we get esta = 1/2 is total = 3/2 NATURE OF FORCED AND FREE INTERNAL TIDES IN THE OCEAN It has been shown by A. Defant.’~ and B. Haurwitz a0: that, for a two-lay- ered ocean, forced internal tidal waves in an unlimited ocean play no role outside of a very narrow band at those geographical latitudes where w, =f. The defini- tions of these symbols are: @,-= frequency of the tide = generating force and f=20 sing. At these latitudes, however, the wavelength goes to infinity. Therefore, it is believed that internal tidal waves are not forced waves. Taking the tide- generating force as Ko exp[i (kX + wot) | (51) the Defant-Haurwitz theory shows the following unrealistic property: the tide - generating forces on the earth have a wavelength Ag =27/kg, which is generally larger than the ocean basins. The ocean itself, however, is assumed to be infinite. Therefore, the wavelength A, should also be infinite and this means that equation 51 should be reduced to K exp (1 wot). A more realistic model can be obtained in the following way. Assume (1) that the wavelength Xo is larger than any ocean on the earth and not a multiple of the length of the ocean: Ag>2L and AQ 4 2nL; and (2) that the tide- generating force can be expanded into its Fourier components in regard to the basin. 21 22 Forced Internal Waves Starting with the perturbation equations, dU Me ee f x Up+Vp+ pVb+K=0 (52) de. 9 OE ap? 32 0 V-0=0 and eliminating the horizontal components of velocity, pressure, p, and density, p , in order to get a differential equation for the vertical component of velocity w: 4 2) 3 J7u Ow O-w o°w ow Vie ee + 21° Vasu nafs kis he (pipes as at? dz at? dz? S|ER Soke ORV GK a || Wp a —f \ Vx 2a, SAV: 55 Gh (53) z Surface tides are excluded from the boundary conditions so that in the case of a horizontal bottom w=o for z=o and 2=H (54) must hold. The inhomogeneous term in (53) is simplified to ky exp [i(kox+79¥+@ot)] with k,~10 728 em! sec”? (55) where the magnitude of k, follows from the expression 3 2 Rp — 32h p wl Des niu Ros 3 exp [i (koX + No¥ + ct)|gm em“ sec [S(O oo I OY ell fap = 10-4 gm sec 2 em (56) with M=mass of the moon, assuming the mass of the earth to be unity r= distance between the center of the earth and the center of the moon R z= radius of the earth For simplication, we take P=T) = constant, i.e., plz) = Po exp (1 z). Now consider a rectangular basin -L xdy l,m TES XP U7 xe at y ] dxdy ma Ep Ag NB Setting (2L-£2,,) 72B -- md‘) ie a aa (58) 0 0 we have after integration sina, sin B 2p =o) —= === (59) , (? ay Be and since by assumption A,, is not a multiple of 2L, all hy m are not equal to zero. j The same expansion for w(x,y,z,t) is ; > [inx mmy W (x, y, Z, t) = a) pine Wy (2) exp l ee (60) and with a Hits dw = d?W > on, D> — << Te SO D0" Ore (m/B) 2 which are Kelvin waves which travel in the x direction. The supposition for these cases is that the tide- generating force is expandable in terms of L and B. (2) The case where angular frequency of internal waves is less than Coriolis parameter, 1.e., 2 2 Og f, that is, south of 30°N for the K, -tide and south of 28°N for the 0, -tide. The behavior of free waves in the entire area where w 2f in the case of a variable Coriolis parameter is given below. 4 Suppose f=f(y) and waves w(x,y,z,t)=w(x,y,2) exp (iwt). Then the following equations describe free internal waves: fo} (e) P Pes pee (65) ax 8 P eee age hn (66) oy 25 26 oP [o) [o} {o} iow —gR+—+IT P=0 (67) Oz fsRieeilne 10 (68) 2) (e) (o) du ov Qw al es te Gig CN Cr =0 (69) raed: ° Oure Elimination of a, 0, w, and R yields 2 BU ea GAR a7, Py) BP BaP — + ‘i caus axe ay? Pw? 22 fw 7) ew? — f2 ay Dh 1S 9) ; B DB - . dP - ,0 Or peers i, (Peri Raia P= On 70) where pe and pp — y rd We now consider waves with infinitely long crests, a = 0, and neglect the small terms ——&. 0 ~~ 1. It follows that an gl-w2 dz N 2 , 6 2 fe) pi Haden (Mae NS Le atl w2 —f2 lady? w2-f2 9% ar =a ll a dz OT a = P‘\=0 (71) al — w2 with a separation By, z)=G (y) Piz) (72) yields 2G er iamaG 2 LAS SUS UGE NOS By Gadi (73) dy? w*—f* dy a A 2 oe dP ar: CO lielperay pe nO (74) dz? dz el = w? After differentiation of (74) under consideration of (67) , (68) , and - os <) Because of the smallness of f’ and f’’,Y(4 is negligible in regard to K? for all areas outside of & , where w=f(&) . Therefore, we suppose Y(é) = 0 for these regions and get Y(€) =Yoexp (ik), w > f (81) or G(y) = Go ear gifts BN 1/2 (w? — f?) expfic’? i la? = i (y) dy (82) In order to find the influence of the singularity at & , we consider (78) to be an inhomogenous equation d*y aS 4 KAY = WHEN (83) dé with the solution y (0) Y(&)=Y(0)cos RE + ; Tepes sin RE + = sin k (E— €*) V(E*) YEH dé* (84) re, 0 YT has the character of a 6 — function: 27 Ik pei H 1/2 Me = SEG), == || [w? — f2ly)] dy, w= f(y) (85) YA) Therefore, equation 84 can be solved: Y(é,) YO). Y (€) = Y(0) cos k€ + sin ké + sin k(é— &,) (86) This solution shows that at €=€, , given by w=f , a reflected wave is created which travels back into the area w>f, having the amplitude Med , the wave number Fk , and the phase kg, . Because of G=(w*-f2)Y , the vertical component w=G(y) W(z) of the wave vanishes at w=f . In the following section it is shown that the spectra of the chain records do not indicate any significant decrease of the amplitudes of the diurnal internal tidal wave at ¢ = 30° or north of it. Therefore, it is believed that the observed internal tidal waves are forced waves. ANALYSIS AND INTERPRETATION OF THERMISTOR CHAIN DATA RECORDED AT A DRIFT STATION As pointed out previously, an advantage of anchor stations is that their data can be interpreted directly by the theory of internal waves. They permit the easiest computation of the amplitudes of the modes. Drift Station 1 At Drift Station 1, a continous temperature-depth recording was made with the NEL thermistor chain by USS MARYSVILLE from 2135 hours on 10 October to 2135 hours on 11 October 1963 at the central position 31°00‘N, 121°00 ‘W. The ship was drifting approximately 1 knot to the southeast, which might have caused a doppler shift in the higher modes. Numerical computations of density are based on a hydrographic station in the nearby area. These data are given in table 1. A Fourier analysis has been made on the depth fluctuations of the isotherms. The spectrum of the mean value for all isotherms is shown in figure 5. Both the diurnal and semidiurnal internal tidal waves have amplitudes of about 6 meters (mean value for the upper 200 meters). They are, therefore, equally important. In order to analyze the contributions of each mode to the resultant amp - litudes, the vertical change of the amplitudes must be decomposed into the modes. This was not done because the chain is only 900 feet long and therefore, the observations did not extend to the bottom. Table 1. HYDROGRAPHIC DATA FOR STATION 1 Date: 9 October 1963. Position: 30°07 “N, 120°10’W. Depth: 3800 meters. Depth (m) Temp. (°C) Salinity (°%) Accepted 1 dp 4-6 dane 29 A, (METERS) —— PERIOD (Hk) ey 2 8 6 4 3 2) 15. 1.2 DRIFT STATION 1 DRIFT STATION 2 ———-— DRIFT STATION 3 HARMONICS Figure 5. Mean amplitude spectrum for the upper 180 meters at Drift Stations 1, 2, and 3. Drift Stations 2 and 3 In October 1963, USS MARYSVILLE studied the situation closer to the coast by making measurements with the thermistor chain at Drift Stations 2 and 3, near Sixty Mile Bank. Each observation was 24 hours long (2145 hours to 2130 hours, 15-16 October; 2345 to 2330, 16-17 October). In the first measurement the drift was about 15 miles in 24 hours (approximately 32 cm/sec); in the second, drift was negligible. Doppler shifting appeared to be very small in the tidal range. Representative hydrographic data for both stations are given in table 2. Each isotherm was subjected to a harmonic analysis. Their mean depths were 32, 40, 45, 49, 56, 76, 102, 142, and 173 meters. The sampling rate was every 15 minutes. Mean values of the computed amplitudes, A, , are shown in figure 5 as a function of the harmonics (lower scale) or the periods (upper scale). It can be seen from these curves that the tidal periods govern the spectrum. We get mean amplitudes, J , of about 6 meters for both the diurnal and semidiurnal in - ternal tides in the upper 180 meters, and this is in good agreement with station 1. For comparison, figure 6 shows the predicted tidal curve at San Diego, California, from 10 to 17 October 1963. The tides are mainly diurnal at the beginning and strongly semidiurnal at the end of the period. It therefore seems reasonable to expect internal tides of both periods to be present at all times, METERS Table 2. HYDROGRAPHIC DATA FOR STATIONS 2 AND 3 Date: 18 October 1963. Position: 32°15’N, 118°20’W. Depth: 1692 meters. Accepted 1 dp \9-6 p dz Depth (m) Salinity (°%,) Temp. (°C) —— n\n nl \y ae 1010 0000 1110 0000 1210 0000 1310 0000 1410 0000 1510 0000 1610 0000 1710 0000 TIME (HR) Figure 6. Predicted tides at San Diego, California, for the period 10 Oct 63-17 Oct 63. 31 32 because they are less influenced by damping. The intensity in the tidal range is about 35m? (approximately 380 ft?) /harmonic. given in table 2. They are shown for the upper 500 meters in figures 7A and B. The eigenvalues, « for n = 1 to n=11, and the corresponding phase velocities, c,, according to the approximate formula given in equation 10, are listed below. z (METERS) The eigenfunctions, W,(z), have been computed using the values of A 100 200 300 400 Eigenvalues (m-! sec) 0.4258 6, = 12.6506 €g = 45.9762 1.6454 "6 = 20.2472 0= bY 1? 4.2178 = UD “11= 70.0884 7.4234 €g = 36.0545 A. MODES 1-6 Figure 7. Representative eigenfunctions W_(z) for the upper 500 meters for Drift Stations 2 and 3. dp dz z(METERS) 4.80 2.44 1.52 1.15 100 200 300 400 A. MODES 1-5. Figure 8. Eigenfunctions W (z) at Anchor Station 4, modes 1- 9. 35 z (METERS) i B. MODES 6-9. Figure 8 (continued). Table 5. CONTRIBUTIONS OF FIRST FOUR MODES TO THE OBSERVED FLUCTUATIONS WITH DIURNAL PERIODS AT STATION 4. Depth (m) 36 BW i i in b Analysis of Internal Tides from a Cross-Like Section To obtain preliminary information on the direction of progress of the internal tides, the thermistor chain was towed in a cross-shaped pattern moving, consecutively, from west to east, east to west, north to south, and south to north. The end points of the cross were 31°54°N, 119°25’W; 31°54’N, 117°10W; 32°50 N, 118° 16 ‘W; and 30°52 ‘N, 118° 16 ‘W. The duration of each leg was about 20 hours. Mean water depth was about 1600 meters. As shown by the spectra at the drift stations, the energy is peaked in the tidal range; therefore, even with these short records, dominant energy shift over frequency came mainly from the tidal peaks. Figures 9 and 10 show the amplitude spectra for the four legs. Because the records are short, high confidence cannot be expected. The spectra were obtained at trial periods lasting from 2 hours to 38 hours. The amplitudes in the periods longer than 12 hours are generally larger in the case of the west- east and the south-north legs than in the other two legs. If their spectral densities are compared at common frequencies, they would imply that the semidiurnal, as well as the diumal internal tidal waves run in a northeasterly direction. This supports the results obtained by H.Summers and K.O. Emery.’ The additional maximum in the east-west and north-south directions in periods near 8 hours might be a reflected wave traveling in a southwesterly direction and having a smaller amplitude than the waves traveling to the northeast. Because the amplitudes are different, we cannot expect standing internal tidal waves in the Gulf of Santa Catalina. In agreement with the results presented on pages 15—20, the energy level is higher in the towed records than in the records from the drift stations. WEST-EAST AMPLITUDES (METERS) HOURS Figure 9. Amplitude spectrum for the legs east-west and west-east. 37: 38 25 SOUTH-NORTH 20 F NORTH-SOUTH AMPLITUDES (METERS) HOURS Figure 10. Amplitude spectrum for the legs north- south and south-north. ANALYSIS OF CHAIN DATA FROM SAN DIEGO TO HAWAII In August 1961, USS MARYSVILLE went from San Diego, California to Honolulu, Hawaii (by the route shown in fig. 11) and recorded temperature dis- tributions in the upper 230 meters with the thermistor chain. The ship’s mean direction was about 255°; mean speed was 6 knots. The data obtained during the cruise were reported fully in reference 11, in which short-period waves of encounter were analyzed for slope and power spectrum. Here, the longer internal tide is given primary consideration. The record selected for the analysis covers the period from 2000 hours on 4 August to 2000 on 17 August. The record was processed as follows: 1. Data from one day’s isotherms form one set. A 24-hour record corres- ponds to about 150 nautical miles. 2. The depths of the isotherms were read from the analog record every 10 minutes, taking mean values (by sight) for these points. 3. The Fourier analysis was carried out using three consecutive sets. The combined sets are overlapping: 1-3, 2-4, 10-12, 11-13. It is assumed that the spectra represent the situation in the centers of these areas. Fourier components 30° ° SS New + + Ney ene Fi | DIURNAL ) 2S EN Pe ies i SS! SEMIDIURNAL 160° 150° 140° 130° 120° 110° Figure 11. Cotidal lines of the semidiurnal tides (after Dietrich, ref. 13) and direction of progress of the internal semidiurnal and diurnal tidal waves on the cruise from San Diego to Hawaii. were computed for each isotherm up to the 40th harmonic. The corresponding periods are 72/n hours. 4. To check the influence of the mean inclination of the isotherms on the spectra, the depth change of the isotherms was computed by taking the difference of the mean values of the first and last 10 hours of each 72-hour record. 5. Mean values, Age for all isotherms of each combined set were computed from the A, . 1) As is well known from hydrographic sections,!* the stationary isotherms are inclined in the upper 1000 meters, increasing in depth toward the west. If the linear depth change of an isotherm over a length L is denoted by A and the Fourier amplitudes of this interval are denoted by a, ,, and b, ,;, then Fourier analysis leads to the amplitude spectrum A 9 A ef z! 2 27 1/2 p Nit 7 im where Bn 6 = (2, st F OL st ] and n= 0, b, a Nn with n = 1,2,... Any Fourier analysis of the chain records considered here is therefore strongly influenced in the long-period range by this stationary inclination. The amplitudes, A,,, of the periodic changes are superimposed on this hyberbolic spectrum of the stationary component of the isotherm. a Table 6 gives the mean depth one A, of the isotherms for each com- bined set, the expected amplitude, Ao, st =~ due to these changes, A, and the analyzed amplitudes, A , from the record. The numbers show that A results mainly from the stationary inclination of the isotherms. 40 Table 6. STATIONARY DEPTH CHANGE A OF THE ISOTHERMS IN THE UPPER 230 METERS, ITS FOURIER AMPLITUDE A, ,, AND THE ANALYZED AMPLITUDE A, OF THE RECORD | DISCUSSION OF RESULTS Figures 12-21 show the analyzed amplitudes A, . The dashed line represents the supposed stationary amplitude distribution due to the inclination of the isotherms. The general shape of the dashed line intersecting the minimum values agrees approximately with a function that is propotional to 1/n. In order to determine the doppler shifts one must know the phase velocity, c, and the direction of the internal waves. Since a hydrographic station was not available for the time, the density distribution from STRANGER station 95 (}=30°20.5'N, \=119°27’ W; depth, 3840 m) was substituted. The phase velocities for the 1-4 modes are : C= 2.19 msec” !, Co le20) msec ~!, C= 0.59 msec, C4= 0.47 msec! Because the actual phase velocities in August 1961 may differ from these values, it is not possible to attribute the higher modes to the peaks of the computed spectra. The rules from which the direction of the internal tidal waves were determined are demonstrated in figure 12. Here, one group of peaks appears in the range between 24 hours and 7.2 hours, another beyond 5.5 hours. It is known from the drift stations that the diurnal and semidiurnal tides are dominant in the area under consideration. For this reason the first group of peaks are identified as the modes of the diurnal internal tides. The first mode is thus assumed to ‘appear at 18 hours, having been shifted from 25 hours. Using equation 26, phase velocity C\= 2.19 m/sec! corresponding to the first mode, and ship velocity AMPLITUDES (METERS) Rees Sh S08 eS! Se Ss Gy Se ae oe eee Ga NN TS NSN SNS NE SD aaa DIURNAL TIDES DIRECTION: 0° 1234 5 MODE SEMIDIURNAL TIDES “1 DIRECTION: 45° | 5 0 fe 0 5 10 15 20 D5) 30 35 HARMONICS ——= Figure 12. Mean amplitudes A, for the upper 200 meters, San Diego-Honolulu. Set 1-3, 4 Aug 61, 2000-7 Aug 61, 2000. 41 AMPLITUDES (METERS) = jo) nn DIURNAL TIDE DIRECTION: 0° SEMIDIURNAL TIDES me aS DIRECTION: 45° \ HARMONICS ——> Figure 13. Mean amplitudes An for the upper 200 meters, San Diego-Honolulu. Set 2-4, 5 Aug 61, 2000-8 Aug 61, 2000. AMPLITUDES (METERS) = oO (Sa) DIURNAL TIDES DIRECTION: 0° AO AS MODE | SEMI DIURNAL DIRECTION: 3 HARMONICS —=— Figure 14. Mean amplitudes A, for the upper 200 meters, San Diego-Honolulu. Set 3-5, 6 Aug 61, 2000-9 Aug 61, 2000. 43 44 AMPLITUDES (METERS) 10.29 123 45 MODE Wt DIURNAL TIDES DIRECTION: 0° Figure 15. Mean amplitudes A, for the upper 200 meters, San Diego- Honolulu. Set 4-6, 7 Aug 61, 2000-10 Aug 61, 2000. SEMIDIURNAL TIDES DIRECTION: 45° 3 20 25 30 HARMONICS ——> 35 S8'l CL 35 T 3 DIURNAL TIDES DIRECTION: 15° f peeieeee rean: eS Ee ee eae fe ai SIS [Voy (=) Ve) (ap) (SYS LAW) SAGNLITdWY HARMONICS —> 45 Figure 16. Mean amplitudes A,, for the upper 200 meters, San Diego-Honolulu. Set 6-8, 9 Aug 61, 2000-12 Aug 61, 2000. 46 AMPLITUDES (METERS) ron SY Ss = DIURNAL TIDES (NO DOPPLER SHIFTS) DIRECTION: 340° ac 0 5 10 US) 20 D5 30 35 HARMONICS —> Figure 17. Mean amplitudes A, for the upper 200 meters, San Diego- Honolulu. Set 7-9, 10 Aug 61, 2000-13 Aug 61, 2000. AMPLITUDES (METERS) 10.29 S & SO S G&G @& G@ CG) Tf ©) BG Sey mH iS SED LOU CON IGN Seti Get CON NOU Stl GO i Se OSNTOO (oe) Wo) MR) SP OSS Ge Ge) GN ONS GNI me Oa Oa (=) oO wy S Sm © f& fo) N So S)- i>) 1%) Vo i xt — oN , fe) to) S| Om MO mM A N GN 72 24 14.4 N — DIURNAL TIDES (NO DOPPLER SHIFTS) 10 DIRECTION: 340° 5 0 0 5 10 15 20 25 30 35 HARMONICS ——>= Figure 18. Mean amplitudes A, for the upper 200 meters, San Diego-Honolulu. Set 8-10, 11 Aug 61, 2000-14 Aug 61, 2000. 47 DIURNAL TIDES 1ST MODE DIRECTION: 325° (SYSLAW) SAGNLITdWYV HARMONICS ————> for the upper 200 meters, San Diego-Honolulu. Set 9-11, 8 c ke Wye os vcs > 2 oO cS 5) ee Sue 200 i) is =A GS tS —~ Oo g3 AG “sn AMPLITUDES (METERS) 72 14.4 10.29 24 8.00 6.55 5.54 4.80 4.24 3.79 3.43 3.13 2.88 2.67 2.48 2.32 2.18 2.06 DIURNAL TIDES 1ST MODE DIRECTION: 325° 1k95 1.85 0 5 10 15 20 25 30 35 HARMON! CS ————> Figure 20. Mean amplitudes A, for the upper 200 meters, San Diego- Honolulu. Set 10-12, 12 Aug 61, 2000-16 Aug 61, 2000. 49 50 AMPLITUDES (METERS) 10.29 DIURNAL TIDES 1ST MODE DIRECTION: 305° 0 2) 10 15 20 25 30 35 HARMON!ICS ——= Figure 21. Mean amplitudes A, for the upper 200 meters, San Diego- Honolulu. Set 11-13, 14 Aug 61, 2000-17 Aug 61, 2000. U=6 knots=3.1 m/sec, cos a = 0.2740 is found. Therefore, the angle between the ship’s direction (255°) and the direction of the internal diurnal tidal wave is 74°. The wave travels in either a northerly or a southeasterly direction. The northerly direction has been accepted in consideration of the surface tide. The doppler shift up to the 5th mode has been computed with the same angle, 74° (indicated by arrows in fig. 12). The determination of the direction of the semidiurnal internal waves has been carried out in the same way, assuming that the 12.4-hour period is shifted to the second group of peaks. The results are shown in figures 12-21. The figures show that a systematic shift occurs: the diurnal internal tidal waves appear at periods between about 18 and 6 hours in sets 1-3, 2-4, 3-5, and 4-6, which represent positions north of 28° latitude. Therefore, they always travel in the same direction, namely, to the north. In set 6-8 a shift to 14.4 hours occurs but the waves in the following sets turn to the northwest, as indicated by the peak that occurs at 24 hours in sets 7-9 and 8-10, and at 36 hours in sets 9-11 and 10-12. In set 11-13 the peak seems to be shifted even further to the long-period range, which indicates that the wave has turned more into the ship’s direction. In regard to the semidiurnal internal tidal waves, one finds an angle of 67° between the ship’s direction and the direction of wave travel. Again there is an uncertainty of + 7 and the direction that agrees best with the direction of surface tides is accepted. This leads to 45° for the direction of internal wave progress. The amplitudes in the semidiurnal range decrease with increasing set number; they cannot be recognized in the sets following set 4-6. Figure 11 shows the ship’s route, the analyzed direction of the diurnal (25 hour) and semidiurnal (12.4 hour) internal tidal waves and the cotidal lines of the semidiurnal surface tides (as given by G. Dietrich; see ref 13). The results in regard to semidiurnal internal tides agree with the theoretical concept given previously: *(1) in general they have the direction of the surface tides as long as these can be considered to be forced by the tide - generating force, and (2) their amplitude decreases toward Hawaii and their direction cannot be determined for the western part of the cruise, because two tidal domains seem to be present. There should be one internal tidal wave coming from the northwest and another one from the southeast; the latter belongs to the amphidromic system centered near 5°S, 155°W. Therefore, both waves may cancel or at least merge in such a way as to greatly reduce the amplitudes. The diurnal surface tides travel toward the west near Hawaii and in a north- westerly direction elsewhere on the ship’s track, as shown in Dietrich’s phase diagram for the surface tide.!3 This agrees with the expected directions south of 28°N. North of this latitude only internal Kelvin waves are possible, and since the coastline is north-south, it is expected that these waves would also travel in a south-to-north direction. This is very pronounced in all spectra north of 28°N. *See pages 21-28. ol 52 CONCLUSIONS The study has shown that the resolution of the Fourier amplitude spectra is not high enough to permit accepting them, and the conclusions they suggest, with complete confidence. The chain records do not permit interpretation of vertical changes in the amplitudes by the eigenfunctions. The actual density distribution is available to compute phase velocities of the internal waves in the area under consideration. However, the continous shift in the spectrum supports the theoretical results described in the section on forced internal waves (pp. 16-20 ). Therefore, the numerical results give a tentative picture which can be checked by additional measurement. RECOMMENDATIONS 1. Verify the theory of internal waves of tidal period with additional measurements with the thermistor chain. 2. Fora complete analysis of the various modes of internal waves, ex- tend measurement of the thermal structure to the sea floor. 3. Supplement the study of internal waves by the use of current meters and salinometers mounted on the chain or at anchored stations; use the date produced to increase the usefulness of thermistor-chain data in the study of the ocean structure (sound-velocity structure) controlled by non- periodic motion such as advection. BIBLIOGRAPHY 1. Defant, A., ‘‘Reality and Illusion in Oceanographic Surveys,’’ Journal of Marine Research, v. 9, p. 120-138, 1950 wo Reid, J.L., Jr., ‘‘Observations on Internal Tides in October 1950,”’ American Geophysical Union. Transactions, v. 37, p. 278-286, June 1956 3. Rudnick, P. and Cochrane, J.D., ‘ ‘Diurnal Fluctuations in Bathythermo - grams,’’ Journal of Marine Research, v. 10, p. 257-262, 1951 4. Emery, K.O., The Sea Off Southern California; A Modern Habitat of Petroleum, p. 126-130, Wiley, 1960 5. Arthur, R.S., ‘‘Oscillations in Sea Temperature at Scripps and Oceanside Piers,’’? Deep-Sea Research, v. 2, p. 107-121, 1954 6. Lee, O.S., ‘‘Observations on Internal Waves in Shallow Water,’’ Limnology and Oceanography, v. 6, p. 312-321, July 1961 7. Summers, H.J. and Emery, K.O., ‘‘Internal Waves of Tidal Period Off Southern California,’’ Journal of Geophysical Research, v. 68, p. 827-839, 1 February 1963 8. Navy Electronics Laboratory Report 1114, The USNEL Thermistor Chain, by E.C. LaFond, 20 June 1962 9. Defant, A., ‘*The Origin of Internal Tide Waves in the Open Sea,’’ Journal of Marine Research, v. 9, p. 111-119, 1950 10. Haurwitz, B., ‘‘Internal Waves of Tidal Character,’’ American Geophysical Union. Transactions, v. 31, p. 47-52, February 1950 11. Navy Electronics Laboratory Report 1130, Measurements of Thermal Structure Off Southern California With the NEL Thermistor Chain, by E.C. LaFond and A.T. Moore, 28 August 1962 12. Oceanic Observations of the Pacific: 1955, The NORPAC ATLAS: (prepared by the NORPAC Committee) Berkeley, University of California Press, Tokyo, University of Tokyo Press, 1960, fig. 83 13. Dietrich, G., ‘*Die Schwingungssysteme der Halb-und Eintagigen Tiden in den Ozeanen,’’ Berlin. Universitat. Institut fiir Meereskunde. Veroffentlichungen. Series A. Geographisch-Naturwissenschaftliche Reihe, v. 41, 1944 Groen, P., ‘ ‘Contribution to the Theory of Internal Waves,’? Koninklijk Nederlands Meteorologisch Instituut de Bilt. Mededelingen en Verhandelinge n, Ser. B, v. 2, No. 11, 1948 Lockheed Aircraft Corporation Report LR 16795, Spectra of Internal Waves Over Basins and Banks Off Southern California, by A.J. Carsola and others, March 1963 REVERSE SIDE BLANK 53 is tay ital UNCLASSIFIED Security Classification DOCUMENT CONTROL DATA - R&D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified) 1. ORIGINATIN G ACTIVITY (Corporate author) 2a. REPORT SECURITY CLASSIFICATION ' UNCLASSIFIED 26. GROUP Navy Electronics Laboratory San Diego, California 92152 3. REPORT TITLE INTERNAL TIDES OFF SOUTHERN CALIFORNIA 4. DESCRIPTIVE NOTES (Type of report and inclusive dates) Research and Development Report, August 1963-February 1964 5. AUTHOR(S) (Last name, first name, initial) Krauss, W. 6. REPORT DATE Ja. TOTAL NO. OF PAGES 7b. NO. OF REFS 6 July 1966 53 15 8a. CONTRACT OR GRANT NO. 94. ORIGINATOR’'S REPORT NUMBER(S) 1389 9b. OTHER REPORT NO(S) (Any other numbers that may be assigned this report) Distribution of this document is unlimited. b. PRosectT NO.OR 104 03 01, Task 0580 (NEL L40461) @ 10. AVAIL ABILITY/LIMITATION NOTICES 11. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Naval Ship Systems Command Department of the Navy 13. ABSTRACT A method accounting for doppler-shift effects was used to interpret data recorded from San Diego to Hawaii by moving thermistors. Results lead toa reasonable picture of the internal tides in that area of the Pacific Ocean. Internal tidal waves are an important component in the spectra at tidal frequen- cies in the sea off southern California. It is likely that they travel in a north- easterly direction. DD .528. 1473 o101-207-c200 UNCLASSIFIED Security Classification UNCLASSIFIED Security Classification KEY WORDS Tides - Pacific Ocean Internal Waves INSTRUCTIONS 1. 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Each paragraph of the abstract shall end with an indication of the military security classification of the in- formation in the paragraph, represented as (TS), (S), (C), or (U). There is no limitation on the length of the abstract. How- ever, the suggested length is from 150 to 225 words. 14. KEY WORDS: Key words are technically meaningful terms or short phrases that characterize a report and may be used as index entries for cataloging the report. Key words must be selected so that no security classification is required. Identi- § fiers, such as equipment model designation, trade name, military project code name, geographic location, may be used as key words but will be followed by an indication of technical con- text. The assignment of links, rales, and weights is optional. UNCLASSIFIED Security Classification GaldISSVIONN S! 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Sapl} |eUsajU! aU} JO a4nyaid ajqeuosead e 0} peal S}INSeY S10} -S|W1aU} BUIAOW Aq [leMeH 0} Obaig UeS Wo4y papsodad eyep yasd -12]U! 0} pasn Sem $}ajJa yJ!US-Jajddop 40) busyunod9e pouyaw Y dal4ISSVIONN "99 Inf 9 ‘dg ‘ssneay “MAG “WINYOIITVD NYSHINOS 440 SAGIL TWNYILNI 68ET }uoday ‘ylye9 ‘obalg ues ‘*qey] $91u04}9819 ANeN CHIEF OF NAVAL MATERIAL MAT 033 COMMANDER, NAVAL SHIP SYSTEMS COMMAND SHIPS 1610 SHIPS 1620 SHIPS 1631 SHIPS 2021 (2) SHIPS 204113 COMMANDER, NAVAL FACILITIES ENGINEERING COMMAND CODE 42310 COMMANDER, NAVAL AIR SYSTEMS COMMAND AIR 5330 AIR 5330 AIR 5330 COMMANDER, ORD 9132 ORD 9132 ORD 03¢ ORD 0322 FASS COMMANDER, NAVAL SHIP ENGINEERING CENTER CODE 6420 CODE 6440 CODE 6452E CODE 6454 CHIEF OF NAVAL PERSONNEL PERS 118 CHIEF OF NAVAL OPERATIONS OP-312 F OP-O7T OP-701 oP-71 OP-03EG OP-0985 OP-311 OP-322C OP-702C op 716 OP-922Y4C1 CHIEF OF NAVAL RESEARCH CODE 416 CODE 418 CODE 427 CODE 466 CODE 468 CODE 493 COMMANDER IN CHIEF US PACIFIC FLEET COMMANDER IN CHIEF US ATLANTIC FLEET COMMANDER OPERATIONAL TEST AND EVALUATION FORCE DEPUTY COMMANDER OPERATIONAL TEST + EVALUATION FORCE», PACIFIC COMMANDER SUBMARINE FORCE US PACIFIC FLEET US ATLANTIC FLEET DEPUTY COMMANDER SUBMARINE FORCE> US ATLANTIC FLEET COMMANDER ANTISUBMARINE WARFARE FOR US PACIFIC FLEET COMMANDER FIRST FLEET COMMANDER SECOND FLEET COMMANDER TRAINING COMMAND US ATLANTIC FLEET OCEANOGRAPHIC SYSTEM PACIFIC COMMANDER SUBMARINE DEVELOPMENT GROUP TWO COMMANDER KEY WEST TEST + EVALUATION DETACHMENT DESTROYER DEVELOPMENT GROUP PACIFIC FLEET AIR WINGS» ATLANTIC FLEET SCIENTIFIC ADVISORY TEAM US NAVAL AIR DEVELOPMENT CENTER NADC LIBRARY US NAVAL MISSILE CENTER TECHe LIBRARY PACIFIC MISSILE RANGE /CODE 3250/ US NAVAL ORDNANCE LABORATORY LIBRARY SYSTEMS ANALYSIS GROUP OF THE ASW R-D PLANNING COUNCIL» CODE RA US NAVAL ORDNANCE TEST STATION PASADENA ANNEX LIBRARY CHINA LAKE (RUDC-2) (RUDC-3 ) NAVAL ORDNANCE SYSTEMS COMMAND (DLI-304) INITIAL DISTRIBUTION LIST ABERDEEN PROVING GROUND» REDSTONE SCIENTIFIC CENTER US ARMY ELECTRONICS R-D LABORATORY AMSEL-RD—MAT COASTAL ENGINEERING RESEARCH CENTER MDe 21005 INFORMATION CORPS OF ENGINEERS» US ARMY HEADQUARTERS» US AIR FORCE AFRSTA AIR UNIVERSITY LIBRARY AIR FORCE EASTERN TEST RANGE 7AFMTC TECH LIBRARY - MU-135/ AIR PROVING GROUND CENTER» PGBPS-12 H@ AIR WEATHER SERVICE WRIGHT-PATTERSON AF BASE SYSTEMS ENGINEERING GROUP (RTD) UNIVERSITY OF MICHIGAN OFFICE OF RESEARCH ADMINISTRATION UNIVERSITY OF MIAMI THE MARINE LABe LIBRARY MICHIGAN STATE UNIVERSITY COLUMBIA UNIVERSITY HUDSON LABORATORIES LAMONT GEOLOGICAL OBSERVATORY DARTMOUTH COLLEGE RADIOPHYSICS LABORATORY CALIFORNIA INSTITUTE OF TECHNOLOGY JET PROPULSION LABORATORY HARVARD COLLEGE OBSERVATORY OREGON STATE UNIVERSITY DEPARTMENT OF OCEANOGRAPHY UNIVERSITY OF WASHINGTON DEPARTMENT OF OCEANOGRAPHY FISHERIES-OCEANOGRAPHY LIBRARY NEW YORK UNIVERSITY DEPT OF METEOROLOGY + OCEANOGRAPHY UNIVERSITY OF MICHIGAN DIRECTOR» COOLEY ELECTRONICS LAB DRe JOHN Ce AYERS UNIVERSITY OF WASHINGTON DIRECTOR», APPLIED PHYSICS LABORATORY OHIO STATE UNIVERSITY PROFESSOR Le Ee BOLLINGER UNIVERSITY OF ALASKA GEOPHYSICAL INSTITUTE UNIVERSITY OF RHODE ISLAND NARRAGANSETT MARINE LABORATORY YALE UNIVERSITY BINGHAM OCEANOGRAPHIC LABORATORY FLORIDA STATE UNIVERSITY OCEANOGRAPHIC INSTITUTE UNIVERSITY OF HAWATI HAWAII INSTITUTE OF GEOPHYSICS ELECTRICAL ENGINEERING DEPT HARVARD UNIVERSITY GORDON MCKAY LIBRARY A+M COLLEGE OF TEXAS DEPARTMENT OF OCEANOGRAPHY THE UNIVERSITY OF TEXAS DEFENSE RESEARCH LABORATORY ELECTRICAL ENGINEERING RESEARCH LAB HARVARD UNIVERSITY UNIVERSITY OF CALIFORNIA-SAN DIEGO SCRIPPS INSTITUTION OF OCEANOGRAPHY MARINE PHYSICAL LAB PENNSYLVANIA STATE UNIVERSITY ORDNANCE RESEARCH LABORATORY NAVAL WARFARE RESEARCH CENTER STANFORD RESEARCH INSTITUTE MASSACHUSETTS INST OF TECHNOLOGY ENGINEERING LIBRARY MIT-LINCOLN LABORATORY RADIO PHYSICS DIVISION THE JOHNS HOPKINS UNIVERSITY APPLIED PHYSICS LABORATORY INSTITUTE FOR DEFENSE ANALYSES FLORIDA ATLANTIC UNIVERSITY US NAVAL WEAPONS LABORATORY KXL LIBRARY PEARL HARBOR NAVAL SHIPYARD PORTSMOUTH NAVAL SHIPYARD PUGET SOUND NAVAL SHIPYARD SAN FRANCISCO NAVAL SHIPYARD USN RADIOLOGICAL DEFENSE LABORATORY DAVID TAYLOR MODEL BASIN /LIBRARY/ US NAVY MINE DEFENSE LABORATORY US NAVAL TRAINING DEVICE CENTER CODE 365H» ASW DIVISION USN UNDERWATER SOUND LABORATORY LIBRARY CODE 905 ATLANTIC FLEET ASW TACTICAL SCHOOL USN MARINE ENGINEERING LABORATORY US NAVAL CIVIL ENGINEERING LABs L54 US NAVAL RESEARCH LABORATORY ’ CODE 2027 CODE 5440 US NAVAL ORDNANCE LABORATORY CORONA USN UNDERWATER SOUND REFERENCE LAB. US FLEET ASW SCHOOL US FLEET SONAR SCHOOL USN UNDERWATER WEAPONS RSCH & ENG. STATION OFFICE OF NAVAL RESEARCH PASADENA US NAVAL SHIP MISSILE SYSTEMS ENGINEERING STATION CHIEF OF NAVAL AIR TRAINING USN WEATHER RESEARCH FACILITY US NAVAL OCEANOGRAPHIC OFFICE SUPERVISOR OF SHIPBUILDING US NAVY GROTON US NAVAL POSTGRADUATE SCHOOL LIBRARY(CODE 0384) DEPT» OF ENVIRONMENTAL SCIENCES OFFICE OF NAVAL RESEARCH BR OFFICE LONDON BOSTON CHICAGO SAN FRANCISCO FLEET NUMERICAL WEATHER FACILITY US NAVAL APPLIED SCIENCE LABORATORY CODE 92005 ELECTRONICS DIVISION CODE 9832 US NAVAL ACADEMY : ASSISTANT SECRETARY OF THE NAVY R+D US NAVAL SECURITY GROUP HDQTRS(G43) ONR SCIENTIFIC LIAISON OFFICER WOODS HOLE OCEANOGRAPHIC INSTITUTION INSTITUTE OF NAVAL STUDIES LIBRARY AIR DEVELOPMENT SQUADRON ONE SUBMARINE FLOTILLA ONE DEFENSE DOCUMENTATION CENTER DOD RESEARCH AND ENGINEERING WEAPONS SYSTEMS EVALUATION DEFENSE ATOMIC SUPPORT AGENCY NATIONAL OCEANOGRAPHIC DATA CENTER US COAST GUARD OCEANOGRAPHIC UNIT COMMITTEE ON UNDERSEA WARFARE US COAST GUARD HDQTRS(OSR=2) ARCTIC RESEARCH LABORATORY WOODS HOLE OCEANOGRAPHIC INSTITUTION US COAST AND GEODETIC SURVEY WASHINGTON SCIENCE CENTER — 23 FEDERAL COMMUNICATIONS COMMISSION US WEATHER BUREAU /VX-1/ fi (20) GROUP. DIRECTOR» METEOROLOGICAL RESEARCH 4p LIBRARY f NATIONAL SEVERE STORMS LABORATORY a! NORMAN» OKLAHOMA 73069 NATIONAL BUREAU OF STANDARDS BOULDER LABORATORIES whe US GEOLOGICAL SURVEY LIBRARY DENVER SECTION US BUREAU OF COMMERCIAL FISHERIES LA JOLLA fi WASHINGTON» De Ceo 20240 WOODS HOLE» MASSACHUSETTS 02543 1 HONOLULU» HAWAII 96812 5 STANFORD» CALIFORNIA 94305 ( TUNA RESOURCES LAB LA JOLLA