372
1 ap
P aX3
aUl
OU2
OU3
- + - + -
OXl
OX2 OX3
-g
= 0
where the non-linear term has been written under an equivalent form.
(14)
(15)
Concerning the boundary conditions, as only 'long waves'can be simulated, variations
of ii can be neglected and the approximation ii 2:: k can be made, so that:
U sing this approximation and a standard empirical parametrization of the wind force,
kinetic condition on the surface is rewritten as follows:
where v= (Vl,V2) is the wind velocity 10m. above the sea surface and
1= Pa(0.75 + 0.067Ivl)10- 3
where Pa is the air density.
The kinetic condition on the bottom is also rewritten as:
where C is the so-called Chezy's constant.
2.3 Vertical Integration
( 16)
(17)
(18)
(19)
In order to obtain a 2D set of equations, the simplified equations (12)-(14) arc integrated
in the vertical.
Let h be the thickness of the fluid layer:
The integration of the mass conservation equation, with the use of the Leibnitz
formula for integrals of partial derivatives together with kinematic conditions (4) and
(7), gives
oh
at+V.(hu)=O inD,
where no approximation has been clone.