EM 1110-2-1100 (Part III)
30 Apr 02
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 Eo 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 αo = 7.5E with the trend of the coast, but after undergoing
refraction, the waves break on a sandy beach with an angle of αb = 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
K
QR '
PR
(ρs & ρ) g (1 & n)
0.60
QR '
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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