10-1
Deep water asymptote
for blocking
10-2
Shallow water asymptote
for blocking
10-3
10-4
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Relative Water Depth, d/L o
Figure 3. Nondimensional blocking speed as function of relative water depth
d/Lo
Asymptotic solutions to the conditions for blocking may readily be
obtained for shallow and deep water. In deep water, that is, kd → ∞,
Equation 20 yields:
1
L=
Lo
(23)
4
and Equation 22 results in:
1
U s cos(δ - α) = - Co
(24)
4
In shallow water, kd becomes small, and various terms in Equations 20 and
22 have to be expanded with respect to this quantity. Omitting terms of order
(kd)2 and higher to obtain an explicit solution, the following approximation is
obtained for the wavelength at blocking (shallow water):
1/ 6
d 9 d
=
(25)
L 32π5 Lo
The corresponding current speed at blocking is given by:
1/ 2
1 d
U s cos(δ - α)
=
(26)
2π Lo
gTa
This relationship is in fact identical to Uscos(d-a) = (gd)1/2. The asymptotes
for deep and shallow water are indicated in Figure 3.
19
Chapter 3 Wave Model
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