Computation of longshore energy flux using LEO current observations

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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]

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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

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Tog! Ib, Welton, dies

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Department of the Army

Coastal Engineering Research Center (CEREN-EV)
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D31181

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March 1980
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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).

To obtain Kelvin (K) readings, use formula:

POS (SVN (UF BS) 20K IS.

“= if ry ; i ( YY a I Ps ;
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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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-29S ‘Il ‘eTIEL ‘I ‘sasseo0r1d Tez079TT *Z ‘BuTAeeuTZue TeISeOD “1
‘ATuo ejep
quZTey eaeM BuTyeerq pue JuezInd sizoysZuoT BuTsn paqetnoTes aq ues Shy
Moy ST}eIep jaoder queseid sayy ‘aTZue eaem BuTyee1q pue ‘potied aaem
‘yy8tey eaem Jo uozjzounz e se 853 207 suotzenbe snofaea seatZ (WdS)
yTenuey_ uotjoeI01g ez0YS ay, Jo » rzezdeyQ ‘wearZ0i1d (OMT) uot eAIeSqO
quewuor~AUg [P1047] ey} WoIy suOT}eAZeSqO Queaino Butsn ‘9854 ‘1030R5
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*10}30eF xNTJ ABi1sue eroYySsZuoT AOF uoTIeATIaq :xTpueddy
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TeIseoD *S*n — pre TeoFuYyDeL) — “wo /Z : “TTF : x~Ppuedde -d [71]
‘O86 ‘29FAAeS uoTJeWAOJUT TeoTu
-Yoo], TBUOTIEN wWorF eTqeTTeAe : ‘ea SpTeTysutadg { azequeD yorResey BUT
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SUOTJBAABSqGO JUaIIND OFT Zutsn xnT}F AZ1aue ai0ys3uoT jo uot zeyndwog
“ag “"T ppoL ‘uo3TeM

L429 GO} “OX BI18cn* £07201
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“9S ‘Il ‘TITL ‘I ‘sesseo0id [ei0;3T1 *Z ‘3uptraeuTSue TeqyseoD ‘|
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moy STTe}Jep Jaodei1 queseid sayy ‘eTsue saem Butyeeaq pue ‘potied saem
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TeBI3sbOD “S'N — PEE TedTuYydeL) — “wd /Z : “TTT : xtpuedde -d [71]
"0861 ‘90TAIeg uoTJeWIOJUT TedTu
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‘Ip “*T ppol ‘uojTeM

£29 E08 nou BI18cn” €0ZOL
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moy STTeqJep yaoderz quasead syy ‘aTSsue aaem Butyeerq pue ‘pofied saem
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qusuUuOATAUG T@A0ZITT 94} WOTF SUOTJEAABSGO JUdsAAIND Butsn Shy £30308;
xn~Tj ASieua esTOYyssuoT 9y} ATOZ pequesead st anbyuyseq TeuoTjejnduoo y
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"086| ‘80TAIeS uot JeWIOFJUT TeoTu
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SuOT}PAIESqGO JUeTIND O_] Butsn xnTJ Adizaua asroyssuoT jo uoyzjeqnduog
“ae **T ppoL ‘uojTeM

£79 €=08 =ou BI18cn* €0ZOL
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xn~Tj A8isue aizoyssuoT ey, 10jJ pequeseid sft enbfuyoeaq Teuotjeqnduos y
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TBISseOD “S*n — pre TeoFuyoey) — “wo /Z : “TTF : x~puedde -d [z|]
‘0861 ‘@0TAIeS uoTJeMAOFUT TeoTu
-Yoe] TBUOTIEN WOIF eTqeTTeae : ‘eA ‘plTety83utads £ taqueg yoTeasay But
-laouTsuqg [TeISeOD *S*n : “BA SAPOATEG 330g — “AP SuOjTeM *T ppoy Aq /
SuOT}BAIeSqgO Quetind OFT Butsn xnTJ ABiIeua aszoyssuoT Fo uote Anduwog
‘Ip “*T ppoy ‘uojTen