*u *

*n*

(60)

1

( zα + *h *) - *h*2 ∇ (∇ ⋅ *u*α,*t *) + *nf*l uα + *nf*t uα uα = 0

2

+

2

(1953) recommended the following empirical relationships for the laminar and

turbulent friction factors:

(1 - *n*)3 ν

(61)

(1 - *n*) 1

(62)

where ν is the kinematic viscosity of water, d is the characteristic stone size, and

αo and βo are empirical constants that range from 780 to 1,500, and 1.8 to 3.6

respectively.

The runup of waves on shorelines provides an important boundary condition

for predicting wave-induced currents and sediment transport in the surf zone. The

runup limit is also important for determining the minimum crest elevation of

coastal structures to prevent overtopping and/or flooding. A simple runup scheme

has been implemented in BOUSS-2D. Dry computational cells (land points) are

assumed to be porous regions where the phreatic surface elevation and volume-

averaged velocities are calculated simultaneously with the fluid motion in the wet

cells. When the phreatic surface elevation exceeds the elevation of the land point

by a specified threshold, the porous cell is considered flooded and treated as a

wet cell during the next time-step. Alternatively, when the free surface elevation

drops below a specified threshold above the bottom elevation of a wet cell, the

wet cell is assumed to be dry and treated as a porous cell during the next

time-step.

BOUSS-2D optionally provides a mechanism to simulate the turbulence and

mixing that occurs in regions with large gradients in the horizontal velocities

such as around the tips of breakwaters. The dissipation term is identical to that

used for wave breaking, i.e., Equation 16. The eddy viscosity is given by

Smagorinsky's (1963) formulation with the turbulent length scale proportional to

the grid size. It can be written as:

25

Chapter 3 Numerical Solution

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