Unsteady waves due to oscillating disturbances in an ice-covered fluid

The dynamic response of an ice-covered fluid to oscillating disturbances was analytically investigated for two-dimensional cases. The initially quiescent fluid of finite depth was assumed to be inviscid, incompressible and homogenous. The thin ice-cover was modelled as a homogeneous elastic plate with negligible inertia. The linearized initial- boundary-value problem was formulated within the framework of potential flow. The solution in integral form for the vertical deflection at the ice-water interface were obtained by means of a joint Laplace-Fourier transform. The asymptotic represent- tations of the wave motion were explicitly derived. It is found that the generated waves consist of the transient and steady-state components. There exists a minimal group velo- city and the transient wave system observed depends on the moving speed of the observer. For an observer moving with the speed larger than the minimal group velocity, there exist two trains of transient waves, namely, the long gravity waves and the short flexural waves, the latter riding on the former. Moreover, the deflections of the ice-plate for an observer moving with a speed near the minimal group velocity were analytically obtained.