Battjes and Janssen (1978) to compute the energy dissipation due to breaking
of random waves was utilized. The longshore current was obtained by
solving the longshore momentum equation with linearized friction and
including driving terms from waves and tides. Wijnberg and Van Rijn (1995)
and Van Rijn and Wijnberg (1996) also computed with the wave action
equation to simulate wave transformation and wave-generated longshore
current across a profile. In these modeling efforts, verification of the model
simulations was done mainly for cases where the interaction between the
waves and consideration of the properties of the longshore current was
relatively minor. For example, no simulations were made for waves
propagating on opposing currents where appreciable shoaling, breaking, and
blocking occurred because of the presence of the current.
In recent years, capabilities have advanced for numerical simulation
of wave-current interaction. For example, there have been a number of
studies on two-dimensional (2-D), spectrally based modeling. It is not the
aim here to cover that development; however, selected studies will be
mentioned in the following because of relevance to the present work. The
verification of such models through comparison to laboratory and field data is
still fairly limited. Holthuijsen, Booij, and Herbers (1989) developed a
steady-state numerical model for hindcasting of waves in shallow water
employing an Eulerian formulation of the spectral action equation. This
model has been employed to simulate some field cases, including a tidal inlet
in the Netherlands (Booij, Holthuijsen, and De Lange 1992) and wave
propagation in the Columbia River entrance (Verhagen, Holthuijsen, and
Won 1992), although the available data sets for verification were limited.
Holthuijsen, Booij, and Ris (1993) extended the work by Holthuijsen, Booij,
and Herbers (1989) by allowing for time variations and more general
properties of the spectrum. This new, 2-D model, known as SWAN, was
employed to calculate the wave height transformation on an opposing current
including blocking (Ris and Holthuijsen 1996), and comparisons were made
with laboratory data from Lai, Long, and Huang (1989). Smith and Smith
(2001) describe application of the STeady-state spectral WAVE model
(STWAVE) (Resio 1987, 1988a, 1988b; Smith, Sherlock, and Resio 2001) to
model waves influenced by the tidal current at the entrance to Ponce de Leon
Inlet, FL. STWAVE simulates the wave-current interaction on a 2-D grid.
Reasonable agreement was found between calculations and measurements on
the ebb shoal.
Modeling Momentum Transport in Breaking
Waves
Several investigations have shown that that the peak of the longshore
current (Visser 1982; Smith, Larson, and Kraus 1993) and the location of
maximum setdown (Bowen, Inman, and Simmons 1968; Van Dorn 1976) are
located more shoreward than what numerical models have tended to predict.
An early hypothesis for this shoreward shift was that the wave energy
dissipation commences at the plunge point rather than at the break point
(Visser 1984). The rationale was that waves in the transition region
(Svendsen, Madsen, and Hansen 1978; Svendsen 1984) between the break
point and the plunge point, where the wave overturns as an organized body or
roller (Sawaragi and Iwata 1974), undergo a steep decrease in height but not
a correspondingly great increase in wave energy dissipation. Roelvink and
Stive (1989) thereafter distinguished between production of turbulence from
organized wave energy through the energy balance equation and the
5
Chapter 2 Brief Literature Review
Previous Page
