Page 241 - Soil and water contamination, 2nd edition

228 Soil and Water Contamination
e x e x
sinh x , H = water depth [L], and L = wave length [L].
w
2
The wave characteristics can be estimated using the following empirical equations (Lijklema,
1991):
W
T 54 k tanh 1 (12.4)
.
7
w 1
g k
1
e x e x
where tanh = the hyperbolic tangent function, defined as tanh x ,
x
e e x
. 0 375 . 0 25
gH gF
k 1 tanh . 0 833 and 1 . 0 077 2 , H = water depth (m),
W 2 W
-1
W = wind speed (m s ), and F = wind fetch length (m).
W 2
H w 283.0 k 2 tanh 2 (12.5)
g k 2
. 0 75 . 0 42
gH gF
where k tanh . 0 53 , and . 0 0125 .
2 2 2 2
W W
gT 2
L w for deep water (H > 0.5 L ) (12.6)
w
w
2
gT w 2 2 H
L tanh for shallow water (12.7)
w
2 L
w
Note that Equation (12.7) needs to be solved iteratively, since the term L is found on both
w
sides of the equation. The maximum bottom shear stress can subsequently be found using:
C u 2 (12.8)
b w f b ,max
where C = a friction coefficient [-], that can be estimated using the following empirical
f
relation:
. 0 75
K n
C 4 . 0 (12.9)
f
A b
where K = a measure of the bottom roughness (m), and A = the amplitude of the wave
n b
motion at the bottom (m):
H w
A (12.10)
b
2 sinh( 2 H / L w )
The measure of the bottom roughness K is defined as the so-called D90 value of the bed

n
sediment particles, i.e. the 90th percentile of the particle size distribution. If the bottom

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