Dally (1980) expressed *E*s in terms of a stable wave height, which is a

function of the water depth, based on laboratory experiments made by

Horikawa and Kuo (1966) for waves breaking on a step-type profile. This

formulation is sufficient for the case of depth-limited wave breaking.

However, if the waves break because of a limiting wave steepness (for

example, by waves shoaling and breaking on an opposing current in deep

appropriate. Thus, *E*s was expressed as a function of *H*b determined from

Equation 12.

Dally (1980) used the following relationships for determining *E*s for

depth-limited wave breaking (linear wave theory),

1

(14)

8

(15)

where

ρ = water density

Γ = an empirical coefficient (found to be 0.4 for typical conditions)

In a traditional criterion for depth-limited incipient wave breaking, the stable

and incipient breaking wave heights at a certain water depth are related

through:

Γ

(16)

γb

This relationship gives *H*s = 0.5*H*b, if the commonly applied values Γ = 0.4

and γb = 0.78 are inserted. Thus, by calculating with Equation 14 together

with Equation 16, a model is obtained that is applicable for both depth- and

steepness-limited wave breaking, where Equation 12 yields the wave height

at incipient breaking at the location of interest. (Note that in a surf zone, this

wave height is different from the limiting wave height where breaking was

initiated.) For shallow water, Equations 16 and 12 reduce to Equation 15, in

accordance with the original formulation by Dally (1980). However, it

remains to validate the proposed generalization, which is the subject of the

next chapter. It is noted that the extension of the energy dissipation model to

waves breaking on a current did not require the introduction of new model

parameters or modifications of existing parameter values. The characteristic

shallow water in accordance with Dally (1980).

Waves propagating on a current may experience blocking if the current is

sufficiently strong and has a component opposing the waves. The criterion

for blocking can be obtained by studying the solution to the dispersion

relationship (Equation 6) for an opposing current and for which only one

17

Chapter 3 Wave Model