EXAMPLE PROBLEM III-2-4

FIND:

Calculate the resulting volumetric longshore transport of sand using measured surf zone velocity.

GIVEN:

Breaking waves have an rms height of 1.8 m (5.9 ft) and there is a persistent longshore current in

the surf zone with mean velocity 0.25 m/sec (0.82 ft/sec) as measured at approximately the mid-surf

position. The width of the surf zone is approximately 75 m (246 ft). Assume the *K *coefficient was

calculated as 0.60.

SOLUTION:

With *H*b rms = 1.8 m (5.9 ft) and *V*R = 0.25 m/sec (0.82 ft/sec), Equation 2-12 gives

and Equation 2-11 gives

From Equation 2-7a,

in which *W *is the width of the surf zone, *V*R is the measured longshore current at a point in the surf zone, *C*f

is a friction coefficient dependent on Reynolds' number and bottom roughness, and *V*o is the theoretical

longshore velocity at breaking for the no-lateral-mixing case. A theoretical velocity distribution for a linear

beach profile that best fits Longuet-Higgins nondimensionalized data is chosen

' 0.2

& 0.714

ln

(III-2-12)

in which *Y *equals the distance to the measured current from the shoreline, and *V*/*V*o equals Longuet-Higgins

dimensionless longshore current velocity for an assumed mixing coefficient equal to 0.4, which agrees

reasonably well with laboratory data. Values of the friction factor *C*f in Equation 2-11 were shown by

Longuet-Higgins to be approximately 0.01, based on laboratory data. Thornton and Guza (1981) calculated

the friction factor using field data measured at Torrey Pines Beach, San Diego, California, and a mean value

of the parameter, averaged over four selected days, was 0.01 with a standard deviation of 0.01. Using

Equations 2-11 and 2-12 with knowledge of breaking wave height, width of the surf zone, longshore velocity

(at some point within the surf zone), distance to the measured longshore velocity, and an assumed friction

factor, the longshore sand transport rate may then be calculated. From a practical standpoint, it is often easier

III-2-20

Longshore Sediment Transport

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