Dally (1980) expressed Es 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, Es was expressed as a function of Hb determined from
Equation 12.
Dally (1980) used the following relationships for determining Es for
depth-limited wave breaking (linear wave theory),
1
Es = ρgH s2
(14)
8
H s = Γd
(15)
where
Hs = stable wave height
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
Hs =
Hb
(16)
γb
This relationship gives Hs = 0.5Hb, 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).
Wave Blocking
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
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