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

(23)

4

and Equation 22 results in:

1

(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

1/ 6

=

(25)

The corresponding current speed at blocking is given by:

1/ 2

1 *d*

=

(26)

2π *L*o

This relationship is in fact identical to *U*scos(d*-*a) = (*gd*)1/2. The asymptotes

for deep and shallow water are indicated in Figure 3.

19

Chapter 3 Wave Model