336
7 Wave Transformation in Ice-Covered Water
--------'\._;
!====== ..... --=::J
r
X
t>
H
z
l
Fig. 7.4. Problem formulation scheme
Problem formulation. Let a homogeneous isotropic ice plate of length
L float on the surface of an ideal fluid (see Fig. 7.4). The coordinate origin is
fixed in the free surface of the fluid and the Z axis is directed vertically downward. The linearized boundary problem for the velocity potential ¢ (x, z, t)
is presented as follows:
'\12¢ = 0;
8¢ = 0.
8z
'
8¢
8z
O z=H;
z=O;
-p(g8¢- 82¢) = - 8p. z = o
az at 2
at '
(7.72)
where g is the gravitational acceleration, p is the pressure on the fluid surface,
p is the water density, ( is the deviation of the free surface, and H is the fluid
depth.
As for the homogeneous and isotropic plate, its displacement from equilibrium satisfies the biharmonic oscillation equation:
p
p'h '
z =0; O Thus, the boundary condition beneath the ice plate can be written in the
form:
z=O; O (7.73)
As for the open water area, the assumption 8pjat = 0 is used and the
boundary condition can be written as follows: