between the wave forcing, bottom friction, and lateral mixing. The wave driving force for the longshore

1 M *S*xy

(II-4-37)

'&

ρ *d *M*x*

where, using linear wave theory,

ρ *g H * 2 cos α sin α

(II-4-38)

8

where *n *is the ratio of wave group speed and phase speed. The variables determining wave-induced

longshore current, as seen in the driving force given in Equations II-4-37 and II-4-38, are the angle between

the wave crest and bottom contours, and wave height. Wave height affects not only longshore velocity, but

also the total volume rate of flow by determining the width of the surf zone.

(3) A simple analytical solution for the wave-induced longshore current was given by Longuet-Higgins

(1970a,b) under the assumptions of longshore homogeneity in bathymetry and wave height, linear wave

theory, small breaking wave angle, uniformly sloping beach, no lateral mixing, and saturated wave breaking

(*H = γ*b d) through the surf zone. Under these assumptions, the longshore current in the surf zone is given

by:

5 π tanβ(

γb g d sin α cos α

(II-4-39)

16 * C*f

where

tan *β** = beach slope modified for wave setup = tan *β/(1+(3γ*b2/8))

(4) The modified beach slope tan *β** accounts for the change in water depth produced by wave setup. The

bottom friction coefficient *C*f has typical values in the range 0.005 to 0.01, but is dependent on bottom

roughness. This parameter is often used to calibrate the predictive equation, if measurements are available.

The cross-shore distribution of the longshore current given by Equation II-4-39 is triangular in shape with

a maximum at the breaker line and zero at the shoreline (Figure II-4-15) and seaward of the breaker line.

Inclusion of lateral mixing smooths the current profile as shown by the dotted lines in Figure II-4-15. The

parameter *V*o in Figure II-4-15 is the maximum current for the case without lateral mixing, and it is used to

nondimensionalize the longshore current.

(5) Komar and Inman (1970) obtained an expression for the longshore current at the mid-surf zone *V*mid

based on relationships for evaluating longshore sand transport rates which is given by Komar (1979):

(II-4-40)

Surf Zone Hydrodynamics

II-4-23

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