measurements is obtained with a smaller value for βD than that recommended

by Dally and Brown (1995), both regarding the shape of the offshore tail and

the distribution in the surf zone. There is still a problem in reproducing the

flat current distribution in the surf zone.

Next, a different formulation for the lateral mixing was investigated to

see if the flat current distribution in the surf zone could be simulated better.

where ε is related to the local wave height and bottom orbital velocity, fairly

well describes the lateral exchange of momentum, especially outside the surf

zone where wave breaking is limited. However, in the surf zone, the mixing

might be underestimated because ε has a weak dependence on the breaking

wave properties. Thus, an alternative expression for the mixing was explored

where ε depends on the roller characteristics.

In turbulence modeling, the diffusion of momentum is typically estimated

from the turbulent kinetic energy *k *according to,

νt = *c* k l

(42)

where

νt = kinematic eddy viscosity

The energy dissipation *D *is typically parameterized as:

(43)

where *c*D = an empirical coefficient.

Assuming that the production of turbulence may be derived from the energy

loss by the roller, estimated as *g*βDmR from Dally and Brown (1995), and that

locally the production and dissipation of turbulence balance each other, the

following expression is obtained,

= ρ*c*D

(44)

where the turbulence produced by the roller was evenly distributed over the

water depth. The largest eddies (containing the most energy) should be on

the order of the water depth, making it reasonable to set *l *≈ *d*. Combining

Equations 42 and 44 yields:

1/ 3

νt = 1/ 3 D R

(45)

61

Chapter 6 Verification of Longshore Current Model