EXAMPLE PROBLEM III-2-7

FIND:

Cross-shore distribution of longshore sediment transport using Equation 2-23.

GIVEN:

Waves in 10-m (32.8-ft) depth have an rms wave height of 2.0 m (6.6 ft), angle of 10 deg to the

shoreline, and wave period 8.5 sec. The beach profile is as given below. Assume the wave height to

water depth ratio for incipient breaking *κ *= 1.0, the stable wave height to water depth ratio for wave

re-formation *Γ*stb = 0.40, the energy flux dissipation rate *γ *= 0.15, the lateral mixing coefficient *Λ*mix = 0.30,

and bottom friction coefficient *C*f = 0.01. The *K *parameter (for use in longshore transport relationships)

was calculated as 0.60.

1

100.0

-0.60

2

111.0

0.10

3

132.0

1.00

4

145.0

1.50

5

156.0

1.70

6

169.0

1.90

7

173.0

1.95

8

186.0

1.85

9

190.0

1.80

10

195.0

1.70

11

199.0

1.75

12

207.0

1.81

13

214.0

2.00

14

246.0

3.10

15

340.0

4.00

SOLUTION:

Part II-3 presents relationships for nearshore wave transformation and Part II-4 discusses the

cross-shore distribution of nearshore currents. Alternately, the PC-based numerical model NMLONG

(see Part II-4 for a complete description) may be used to calculate the cross-shore distribution of total

water depth and longshore current speed over an irregular bottom profile (Kraus and Larson 1991),

which can be used in application of Equation 2-23. Entering the given data set, with 100 computation

points, a cross-shore spacing of 2.0 m (6.6 ft), no wind, and a tidal reference elevation of 0.0, the

cross-shore distribution of waves and currents as shown in Figure III-2-22b is obtained. A reduced

listing of the NMLONG output, chosen to represent the peaks and minima of the wave height and

longshore current distributions, is presented in the first four columns of the following table. The

predicted *q*x(y)/*k*q is shown in the last column and in Figure III-2-22a.

99Example Problem III-2-7 (Sheet 1 of 4)

III-2-44

Longshore Sediment Transport

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