EM 1110-2-1100 (Part III)
30 Apr 02
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 Hb rms = 1.8 m (5.9 ft) and VR = 0.25 m/sec (0.82 ft/sec), Equation 2-12 gives
V/Vo = 0.2 (37.5/75) - 0.714 (37.5/75) ln (37.5/75) = 0.35
and Equation 2-11 gives
PR = [(1025)(9.81)(1.8)(75)(0.25)(0.01)]/[(5π/2)(0.35)] = 1234 N/sec (277 lbf/sec)
From Equation 2-7a,
QR = (0.60)(1234)/[(2650-1025)(9.81)(1-0.4)]
QR = 0.077 m3/sec = 6.7 x 103 m3/day (8.8 x 103 yd3/day)
in which W is the width of the surf zone, VR is the measured longshore current at a point in the surf zone, Cf
is a friction coefficient dependent on Reynolds' number and bottom roughness, and Vo 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
V
Y
Y
Y
' 0.2
& 0.714
ln
(III-2-12)
Vo
W
W
W
in which Y equals the distance to the measured current from the shoreline, and V/Vo 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 Cf 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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