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CETA 80-3 (AD -A0@S $26)
Computation of Longshore Energy Flux Using LEO Current Observations
by Todd L. Walton, Jr.
COASTAL ENGINEERING TECHNICAL AID NO. 80-3 MARCH 1980
WHO]
DOCUMENT ) COLLECTION
U.S. ARMY, CORPS OF ENGINEERS ae COASTAL ENGINEERING 330 RESEARCH CENTER
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SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORM 1. REPORT NUMBER 2. GOVT ACCESSION NO.) 3. RECIPIENT’S CATALOG NUMBER CETA 80-3 4. TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED
COMPUTATION OF LONGSHORE ENERGY FLUX USING LEO CURRENT OBSERVATIONS
Coastal Engineering Technical Aid
6. PERFORMING ORG. REPORT NUMBER
8. CONTRACT OR GRANT NUMBER(s)
7. AUTHOR(S)
Tog! Ib, Welton, dies
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9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of the Army
Coastal Engineering Research Center (CEREN-EV) Kingman Building, Fort Belvoir, Virginia 22060
D31181
12. REPORT DATE March 1980 13. NUMBER OF PAGES
w lO;z
SECURITY CLASS. (of thie report)
11. CONTROLLING OFFICE NAME AND ADDRESS
Department of the Army
Coastal Engineering Research Center
Kingman Building, Fort Belvoir, Virginia 22060
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UNCLASSIFIED
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Approved for public release; distribution unlimited.
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Coastal engineering LEO Longshore energy flux
| ABSTRACT (Continue am reverse side if necessary and identify by block number)
A computational technique is presented for the longshore energy flux factor, Pos, using current observations from the Littoral Environment Observation (LEO) program. Chapter 4 of the Shore Protection Manual (SPM) gives various equations for Py, as a function of wave height, wave period, and breaking wave angle. The present report details how Py, can be calculated using longshore current and breaking wave height data only. An example problem is given for this method
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PREFACE
This report presents a computational technique for determining the long- shore energy flux factor, Pp,, using current observations from the Littoral Environmental Observation (LEO) program. Pegs is discussed in Chapter 4 of the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineer- ing Research Center, 1977). The work was carried out under the coastal engi- neering research program of the U.S. Army Coastal Engineering Research Center (CERC) .
The report was prepared by Dr. Todd L. Walton, Jr., Hydraulic Engineer, under the general supervision of Dr. J.R. Weggel, Chief, Evaluation Branch, Engineering Development Division.
Comments on this publication are invited.
Approved for publication in accordance with Public Law 166, 79th Congress, approved 31 July 1945, as supplemented by Public Law 172, 88th Congress, approved 7 November 1963.
ED MEP Colonel, Corps of Engineers Commander and Director
CONTENTS
CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI). ...... ie:
I INTRODUCTION. 2. lotus Sy) ou orc >. coh oe lene eee) Cheer mio ieee armen 7
II DATA SOURCES t) eupon Sik ce cuene nner) eh Eh age ote) gee 7
Ill DETERMINATION OF LONGSHORE ENERGY FLUX FACTOR. ......... 8
IV GNM UNOS BB 4 6 66 5 5 5 oo 8 oo lf 8 LETERATURE, GETED) 4. 4c: 4) ex paso et TS ie oe ey) Sa)
APPENDIX DERIVATION FOR LONGSHORE ENERGY SETUXQ RAGTOR ii) cyte mee tt
CONVERSION FACTORS, U.S. CUSTOMARY TO METRIC (SI) UNITS OF MEASUREMENT
U.S. customary units of measurement used in this report can be converted to
metric (SI) units as follows:
Multiply by To obtain inches 25.4 millimeters 2.54 centimeters square inches 6.452 square centimeters cubic inches 16.39 cubic centimeters feet 30.48 centimeters 0.3048 meters square feet 0.0929 square meters cubic feet 0.0283 cubic meters yards 0.9144 — meters square yards 0.836 square meters cubic yards 0.7646 cubic meters miles 1.6093 kilometers square miles 259.0 hectares knots 1.852 kilometers per hour acres 0.4047 hectares foot-pounds 1.3558 newton meters millibars 10197) < 105 3 kilograms per square centimeter ounces 28.35 grams pounds 453.6 grams 0.4536 kilograms ton, long 1.0160 metric tons ton, short 0.9072 metric tons degrees (angle) 0.01745 radians Fahrenheit degrees S19 Celsius degrees or Kelvins!
Oooo ooaq*e*S ees SS“ Sau
1To obtain Celsius (C) temperature readings from Fahrenheit (F) readings, use
formula: C = (5/9) (F -32).
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POS (SVN (UF BS) 20K IS.
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COMPUTATION OF LONGSHORE ENERGY FLUX USING LEO CURRENT OBSERVATIONS
by Todd L. Walton, Jr.
I. INTRODUCTION
Prediction of sand transport rates along beaches is necessary to determine dredging quantities at inlets, effective life of various coastal structures such as jetties, and magnitude of erosion-accretion on beaches adjacent to inlets. Most computations of sand transport rate have previously been deter- mined by computing a wave parameter dependent quantity termed the longshore energy flux factor Pp,. Chapter 4 of the Shore Protection Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 1977) gives various equations for Pg. as a function of wave height, wave period, and wave angle with the shoreline at breaking. As wave angle is a difficult param- eter to measure, an alternate approach is to use the longshore current as an independent quantity with which to determine Pps, since the wave angle with the shoreline is explicitly contained within the most acceptable formulas for longshore currents due to breaking waves (e.g., Longuet-Higgins, 1970). The present report incorporates the longshore current model (due to breaking waves) of Longuet-Higgins to determine the longshore energy flux factor, which in turn, can be used to estimate longshore sand transport rates.
II. DATA SOURCE
The computational technique in this report uses current observations from the Littoral Environmental Observation (LEO) program. The LEO program was developed by the Coastal Engineering Research Center (CERC) and is discussed by various investigators (Berg, 1969; Szuwalski, 1970; Bruno and Hiipakka, 1973; and Balsillie, 1975a). In the LEO program nearly simultaneous visual observations of breaker conditions (height, period, angle of approach, and type), local winds, longshore currents, rip currents, and beach geometry are made daily for a year or more. The selection of observation sites is not generally hindered by lack of access to the beach which often limits the use of instrumentation. Thus, depending on availability of trained observers, many sites along a considerable segment of shoreline may be established using LEO techniques. :
The longshore current is estimated by measuring the shore-parallel distance and observing the direction that a sodium-fluoroscein dye packet injected into the surf (between the breakers and shore) travels in 1 minute. Observation of longshore current movement from the dye injections is representative of surface movement at the injection site, but may not always reflect the movement of water at depth or represent the average speed across the surf zone. As LEO measurements include the width of the surf zone as well as the distance from shore to the injection point of the dye, the longshore current can be treated as a point measurement on a spatially variable (across the surf zone) long- shore current, the longshore current chosen in accordance with a theoretical profile having an assumed mixing constant. Balsillie (1975b) has shown that the LEO measurements of longshore currents (across surf zone) correlate very well with longshore currents calculated by the theoretical formula of Longuet- Higgins (1970).
7
ITI. DETERMINATION OF LONGSHORE ENERGY FLUX FACTOR
The following equation is equivalent to equation (4-28) in the SPM when calculating the longshore energy flux factor,
eg HRW Vino CF Po =
where re) = fluid density g = acceleration of gravity Hp = breaking wave height W = width of surf zone VigO = average longshore current due to breaking waves Cr = friction factor (assume 0.91) and
ley = 0.2 (5) + 0.74 ‘e) In (*) (2)
where X is the distance to dye patch from shoreline and (V/Vo)zH is the Longuet-Higgins dimensionless longshore current velocity for an assumed mixing coefficient, P = 0.4, which agrees reasonably well with laboratory data (see Longuet-Higgins, 1970). The derivation of equation (1) is presented in the Appendix, as well as reference to equation (2).
It should be noted that as previous calculation equations for Pps are based on significant wave heights (e.g., Ch. 4 in the SPM) equation (1) should also use significant wave height for breaking wave height. The recorded value of Hp in the LEO observation program is a reasonable approximation to signif- icant breaking wave height. It should also be noted that as the LEO current observations are time-averaged, computing Pp, by the present method may pro- vide a lower value of the longshore energy flux factor than given by equations based on significant breaking wave height to higher powers such as those in Chapter 4 of the SPM.
IV. EXAMPLE PROBLEM
GIVEN: A LEO observation with the following measured values of wave height, longshore current velocity, width of surf zone, and distance of dye patch from the shoreline
Hp = 3.0 feet (0.91 meter)
VzRO = 0.5 foot (0.15 meter) per second W = 150 feet (45.7 meters)
X = 50 feet (15.2 meters)
FIND: Longshore energy flux factor, Pp.
SOLUTION:
(a) Using equation (2) calculate V/Vozy
Wa es at) ( 50 ( =) a = = 0.2 Ge > 0.714 ee) Im ey) = 0235
(b) Now, using equation (1) calculate Pgg.
Pos = CAS) EO 2281) = 55.3 pounds (25.1 kilograms) per second ey (0.33)
(c) The value of Pp, corresponds to a sediment transport rate of 415,000 cubic yards (317,310 cubic meters) per year using the SPM equation (4-40) (Ol=87 5a 103 Pps in feet-per-second system).
(d) Annual average sediment transport rates for any field site would be estimated from LEO with a Pp, value obtained by averaging the Py, values computed for each observation by the above method.
LITERATURE CITED
BALSILLIE, J.H., "Analysis and Interpretation of Littoral Environment Observa- tion (LEO) and Profile Data Along the Western Panhandle Coast of Florida," TM-49, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., Mar. 1975a.
BALSILLIE, J.H., "Surf Observations and Longshore Current Prediction,'' TM-58, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Beiivjioaas., Val. Nove 1975b-
BERG, D.W., "Systematic Collection of Beach Data," Proceedings of the 11th Conference on Coastal Engineering, American Society of Civil Engineers, Vol. 1, 1969, pp. 273-277 (also Reprint 4-69, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., NTIS 697 533).
BRUNO, R.O., and HIIPAKKA, L.W., "Littoral Environment Observation Program in the State of Michigan," Proceedings of the 16th Conference on Great Lakes Research, International Association of Great Lakes Research, 1973, pp. 492- 507 (also Reprint 4-74, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Fort Belvoir, Va., NTIS 777 706).
LONGUET-HIGGINS, M.S., 'Longshore Currents Generated by Obliquely Incident Sea Waves,'' Parts 1 and 2, Journal of Geophystcal Research, Vol. 75, No. 33, Nov. 1970, pp. 6778-6801.
SZUWALSKI, A., "Littoral Environment Observation Program in California, Pre- liminary Report, February-December 1968,'' MP 2-70, U.S. Army, Corps of Engineers, Coastal Engineering Research Center, Washington, D.C., Feb. 1970.
U.S. ARMY, CORPS OF ENGINEERS, COASTAL ENGINEERING RESEARCH CENTER, Shore Proteetton Manual, 3d ed., Vols. I, II, and III, Stock No. 008-022-00113-1, U.S. Government Printing Office, Washington, D.C., 1977, 1,262 pp.
APPENDIX DERIVATION FOR LONGSHORE ENERGY FLUX FACTOR Derivation of equation (1) for longshore energy flux factor:
(a) From Longuet-Higgins (1970)
Vy = (=) (g dp)1/2 (m sin ap cos ap) (A-1) where Vp = longshore current at breaking zone B = a mixing parameter dp = breaking depth m = beach slope ap = breaking wave angle K = ratio of breaking wave amplitude to water depth (b) Using relationship 2k = 2 equation (A-1) becomes Vp = Sa (c;) au m (Gee) > sim Lor (A-2)
(c) Longshore velocity at any point within surf zone can be defined as
v=V, = oe (A-3)
where V is longshore current within surf zone and Vo is theoretical long- shore velocity at breaking, no mixing.
(d) From equation (58) of Longuet-Higgins (1970)
WO _ il Te 6 (A-4) (e) Using equations (A-4), (A-3), and (A-2), longshore velocity is — fw 5 K 1/2 : WS (i) (zz) (c) (x) m (gH,) 1/2 sin 2a, (A-5)
(f) Using the SPM equation (4-28)
p gly” Pos = TIGHT GD sin 2ap (A-6)
where Cy,p equals group wave celerity equals (g ap) 272 linear wave theory; therefore
p gHy,* dp 1/2 p Pos = Het: ee (gH,) 1/2 sin 2ap (A-7)
(g) Using equation (A-2), (A-5), and (A-7) and assuming m = dp,/W
Hh WV C ps ee c NS (A-8)
(als)
(h) The value of (V/Vo) can be assumed equal to that given by Longuet-
Higgins (1970) ts) i co ar
(1) The value of V is measured using LEO technique
V= VEO (A-10)
(j) Equation (A-8) now becomes
H, WV C Pog = Phy IO) (A-11)
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