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.

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