EXAMPLE PROBLEM III-2-3

FIND:

Calculate the potential volumetric longshore sand transport rate along the beach.

GIVEN:

Spectral analysis of wave measurements at an offshore buoy in deep water yields a wave energy

density *E*o of 2.1 x 103 N/m (144 lbf/ft), with a single peak centered at a period *T *= 9.4 sec. At the

measurement site, the waves make an angle of *α*o = 7.5E with the trend of the coast, but after undergoing

refraction, the waves break on a sandy beach with an angle of *α*b = 3.0E. Assume that the *K *coefficient

is 0.60.

SOLUTION:

The group speed of the waves in deep water is given in Part II-1 as

Cgo = gT/4π = 9.8 (9.4) / (4π) = 7.3 m/sec (24.0 ft/sec)

The energy flux per unit shoreline length in deep water is

(ECg)ocosαo = (2.1 x 103)(7.3)cos(7.5E) = 1.5 x 104 N/sec (3.4 x 103 lbf/sec)

The conservation of wave energy flux allows the substitution

(ECg)bcosαb = (ECg)ocosαo

where bottom friction and other energy losses are assumed to be negligible, Equation 2-2 for the

longshore component of the energy flux at the shoreline then becomes

PR = (ECg)b sinαb cosαb = [(ECg)ocosαo]sinαb = (1.5 x 104) sin(3.0E)

PR= 800 *N*/sec (180 lbf/sec)

Spectra yield wave parameters equivalent to rms conditions, and therefore *K *= 0.60 may be used in

Equation 2-7a to calculate the potential volumetric sand transport rate. This gives

(ρs & ρ) *g *(1 & *n*)

0.60

800

(2650 & 1025) (9.81) (1 & 0.4)

QR= 0.050 m3/sec x 3600 sec/hr x 24 hr/day

QR = 4.3 x 103 m3/day (5.7 x 103 yd3/day)

Longshore Sediment Transport

III-2-19

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