7.5 Surface Gravity Wave Interaction with Elastic Ice Floes
335
It should be noted in conclusion that an attempt is undertaken in this
chapter to describe the principal physical mechanisms forming the sea wave
spectrum in the presence of ice cakes. They are: wave refraction, wave energy
dissipation connected with friction between ice floes and non-linear energy
redistribution in the wave spectrum. The obtained results can be a basis for
developing a mathematical model describing the spectral evolution of waves
in sea with ice. This model can be used for wave calculations and forecasts
in the Arctic seas and, particularly, for numerical simulation of phenomena
such as "ice storms", caused by storm wind waves propagating to marginal ice
zones. These are very dangerous for oil platforms and hydraulic structures.
7.5 Numerical Simulation of Surface Gravity Wave
Interaction with Elastic Ice Floes
Surface waves can penetrate from the open sea into regions with marginal
and continuous ice cover. Numerous experimental data of the wave regime in
the presence of ice were obtained during the MIZEX experiment (Wadhams
et al., 1986). Observations of waves penetrating under fast ice were described
by Squire (1984). In particular, it is noted that, under ice cover, long waves
can penetrate large distances, reach considerable amplitudes, and even break
up solid ice fields (Liu & MoHo-Christensen, 1988; Smirnov, 1996).
The methods of simulating the interaction between gravity waves and
an ice field or a semi-infinite ice plate are fairly well worked out (Bukatov
et al., 1984; Fox & Squire, 1991; Lavrenov and Novakov, 2000; Sturova 1998,
2000). In order to estimate the evolution of the wave spectrum in the presence
of ice, an attempt to simulate surface waves in water covered with floating
ice floes of finite length was developed by Masson & LeBlond ( 1989). The sea
state is described by a two-dimensional discrete spectrum. Time-limited wave
growth is obtained by numerical integration of the wave balance equation
using the exact non-linear transfer integral without taking into account the
presence of ice. Wave scattering by a single floe is presented in terms of farfield expressions of diffracted and forced potentials obtained by the Green
function.
The solution of the problem of gravity waves interacting with ice of finite
length encounters certain difficulties. The problem is reduced to simultaneous
solution of the Laplace equation for the fluid and the bending equation for
a thin elastic plate, which includes fourth-order spatial derivatives.
In this monograph a numerical solution of the problem based on the combined method of finite and boundary elements is developed. A problem formulation similar to Meylan & Squire (1994) is used. This makes it possible
to compare calculation results with the analytical solution for some special
cases.
335
It should be noted in conclusion that an attempt is undertaken in this
chapter to describe the principal physical mechanisms forming the sea wave
spectrum in the presence of ice cakes. They are: wave refraction, wave energy
dissipation connected with friction between ice floes and non-linear energy
redistribution in the wave spectrum. The obtained results can be a basis for
developing a mathematical model describing the spectral evolution of waves
in sea with ice. This model can be used for wave calculations and forecasts
in the Arctic seas and, particularly, for numerical simulation of phenomena
such as "ice storms", caused by storm wind waves propagating to marginal ice
zones. These are very dangerous for oil platforms and hydraulic structures.
7.5 Numerical Simulation of Surface Gravity Wave
Interaction with Elastic Ice Floes
Surface waves can penetrate from the open sea into regions with marginal
and continuous ice cover. Numerous experimental data of the wave regime in
the presence of ice were obtained during the MIZEX experiment (Wadhams
et al., 1986). Observations of waves penetrating under fast ice were described
by Squire (1984). In particular, it is noted that, under ice cover, long waves
can penetrate large distances, reach considerable amplitudes, and even break
up solid ice fields (Liu & MoHo-Christensen, 1988; Smirnov, 1996).
The methods of simulating the interaction between gravity waves and
an ice field or a semi-infinite ice plate are fairly well worked out (Bukatov
et al., 1984; Fox & Squire, 1991; Lavrenov and Novakov, 2000; Sturova 1998,
2000). In order to estimate the evolution of the wave spectrum in the presence
of ice, an attempt to simulate surface waves in water covered with floating
ice floes of finite length was developed by Masson & LeBlond ( 1989). The sea
state is described by a two-dimensional discrete spectrum. Time-limited wave
growth is obtained by numerical integration of the wave balance equation
using the exact non-linear transfer integral without taking into account the
presence of ice. Wave scattering by a single floe is presented in terms of farfield expressions of diffracted and forced potentials obtained by the Green
function.
The solution of the problem of gravity waves interacting with ice of finite
length encounters certain difficulties. The problem is reduced to simultaneous
solution of the Laplace equation for the fluid and the bending equation for
a thin elastic plate, which includes fourth-order spatial derivatives.
In this monograph a numerical solution of the problem based on the combined method of finite and boundary elements is developed. A problem formulation similar to Meylan & Squire (1994) is used. This makes it possible
to compare calculation results with the analytical solution for some special
cases.