dissipation of mean turbulent kinetic energy (TKE) calculated in a one-
equation TKE transport model in which the production term for the TKE is
taken from the wave energy balance equation. Nairn, Roelvink, and
Southgate (1990) and Deigaard, Justesen, and Fredsoe (1991) also applied a
one-equation TKE transport model with the governing hydrodynamic
equations to obtain an improved description of the mean water-surface
elevation and undertow.
Smith, Larson, and Kraus (1993) numerically modeled the longshore
current by adding a transport equation for the TKE to the wave energy
balance equation and the cross-shore and longshore momentum equations.
The momentum transport associated with the turbulence was estimated from
the computed distribution of the TKE through parameterization, which
required assumptions concerning the ratios between the turbulent fluctuations
in the different coordinate directions (i.e., degree of isotropy). By including
the turbulent transport in the alongshore momentum equation, a shift in the
driving force was obtained that produced the desired shoreward translation of
the peak in the current distribution. However, because measurements of the
turbulence in breaking waves are rare (probably due to operational
difficulties in the surf zone with suspended sediment), some empirical
coefficients had to be introduced in connection with the parameterization.
The values on these coefficients were essentially determined through
Dally and Brown (1995) developed a mathematical model to describe the
formation and evolution of the roller that appears as waves break and pass
through the surf zone. They argued that the transition region is not created by
the lag between turbulence by breaking and dissipation in the wake, but by a
lag due to the time required to create the roller itself. An energy balance
equation was introduced, including the energy flux from the organized wave
motion and the roller, as well as the energy dissipation in the roller.
Employing this equation, the cross-shore variation in the roller mass flux
could be calculated, from which the momentum transport in the longshore
and cross-shore direction could be obtained (Dally and Osiecki 1994). Based
on the observations of Duncan (1981) of the instantaneous structure of a
breaking wave, the energy dissipation in the roller was parameterized in
terms of the shear between the roller and the underlying fluid. The roller
model of Dally and Brown (1995) involves two empirical parameters, one
speed. The latter is normally assigned the value of unity; that is, the roller
travels with the speed of the wave. The quantity βD has been shown to have a
value of about 0.1 by comparison with laboratory data.
Laboratory and Field Data on Nearshore
Currents
High-quality data sets on nearshore currents suitable for testing a
numerical model such as NMLong-CW are scarce, although in recent years
some laboratory experiments have been carried out with the specific
objective to study waves propagating and breaking on a current (e.g., Smith
et al. 1998; Chawla and Kirby 1999). A few classical data sets (e.g., Kraus
and Sasaki 1979; Visser 1982) on the longshore current are available for
NMLong-CW validation with respect to introducing the roller model and to
investigate wave-current interaction for wave-generated currents, although
6
Chapter 2 Brief Literature Review
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