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.
The expression for the lateral mixing developed by Kraus and Larson (1991),
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
c = empirical coefficient
l = length scale of the turbulent eddies
The energy dissipation D is typically parameterized as:
k 3/ 2
D = ρcD
(43)
l
where cD = an empirical coefficient.
Assuming that the production of turbulence may be derived from the energy
loss by the roller, estimated as gβDmR from Dally and Brown (1995), and that
locally the production and dissipation of turbulence balance each other, the
following expression is obtained,
gβD mR
k 3/ 2
= ρcD
(44)
d
l
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
c gβ m
νt = 1/ 3 D R
(45)
d
cD ρ
61
Chapter 6 Verification of Longshore Current Model