sources for waves shoaling on laboratory sloping beaches in the absence of
an imposed external current.
Several different models are available to calculate the energy dissipation
produced by wave breaking for time-averaged conditions without a current
present (e.g., Goda 1975; Battjes and Janssen 1978; Dally 1980; Mizuguchi
1980; Thornton and Guza 1983; Svendsen 1984). For waves breaking on a
current, less work has been done to quantify the modification by the current
on the energy dissipation, although several laboratory studies have been
conducted recently on the topic (Smith et. al 1998; Chawla and Kirby 1998,
2000). Chawla and Kirby (1998, 1999) showed that the Battjes and Janssen
(1978) model as well as the Thornton and Guza (1983) model successfully
reproduce wave height decay due to breaking on an opposing current in deep
to intermediate water depths, although some adjustment of the original
coefficient values was required.
Here, the model proposed by Dally (1980) and further developed by
Dally, Dean, and Dalrymple (1985) and Dally (1990, 1992) is extended to
describe energy dissipation by breaking waves in arbitrary water depth
including the presence of a current. The advantages of the Dally-type model
may be summarized as:
a. Relative constancy of optimum values for the two empirical
parameters included in the model, independent of wave and beach
conditions (implying that application without calibration to a specific
site will yield reliable results).
b. Possibility of describing wave reformation in a straightforward and
physically based manner.
c. Capability of generalization for describing random waves without a
priori assumptions regarding the probability distribution of waves in
the surf zone.
. Reliability demonstrated
in numerous independent
applications to a
wide range of hydrodynamic and beach conditions for both small-
scale and large-scale laboratory data and field data, covering both
monochromatic and random waves.
Generalizing to arbitrary water depth and situation of the presence of a
current, the wave energy dissipation produced by breaking according to Dally
(1980) may be expressed as:
(E - Es )Cgr
κ = empirical coefficient (found to be 0.15 for typical conditions)
E = wave energy
Es = stable wave energy below which breaking ceases and
wave reforming occurs
dD = characteristic length scale for the energy dissipation
(= d in the original formulation by Dally 1980)
In the presence of a current, it is the relative group speed that determines the
Chapter 3 Wave Model