7.2. TWO-DIMENSIONAL GOVERNING EQUATIONS
335
Figure 7.1: Two-Dimensional Wave Flume Definition Sketch.
the appropriate boundary conditions. In the two-dimensional Cartesian
coordinate system depicted in Figure 7.1 the Laplace equation is given in
terms of the velocity potential as
Laplace Equation (in the fluid domain)
d2
dx2
dz2
(7.1)
where the velocity potential is (t> — (x,z,t). The bottom boundary condition and the free surface boundary conditions are given by the following
well-known expressions from classical wave theory
Bottom Boundary Condition (at z = —h)
d
(7-2)
= 0
335
Figure 7.1: Two-Dimensional Wave Flume Definition Sketch.
the appropriate boundary conditions. In the two-dimensional Cartesian
coordinate system depicted in Figure 7.1 the Laplace equation is given in
terms of the velocity potential as
Laplace Equation (in the fluid domain)
d2
dx2
dz2
(7.1)
where the velocity potential is (t> — (x,z,t). The bottom boundary condition and the free surface boundary conditions are given by the following
well-known expressions from classical wave theory
Bottom Boundary Condition (at z = —h)
d
(7-2)
= 0