Resonant destabilization of a floating homogeneous ice layer

We show that a homogeneous elastic ice layer of finite thickness and infini te horizontal extension floating on the surface of a homogeneous water laye r of finite depth possesses a countable unbounded set of of resonant freque ncies. The water is assumed to be compressible, the viscous effects are neg lected in the model. Responses of this water-ice system to spatially locali zed harmonic in time perturbations with the resonant frequencies grow at le ast as roott in the two-dimensional (2-D) case and at least as Int in the t hree-dimensional (3-D) case, when time t --> infinity. The analysis is base d on treating the 3-D linear stability problem by applying the Laplace-Four ier transform and reducing the consideration to the 2-D case. The dispersio n relation for the 2-D problem D(k, omega) = 0, obtained previously by Brev do and Il'ichev [10], is treated analytically and also computed numerically . Here Ic is a wavenumber, and omega is a frequency. It is proved that the system D(k, omega) = 0, D-k(k, omega) = 0 possesses a countable unbounded s et of roots (k, omega) = (0, omega (n)), n is an element of Z, with Im omeg a (n) = 0. Then the analysis of Brevdo [6], [7] [8], [9], which showed the existence of resonances in a homogeneous elastic waveguide. is applied to s how that similar resonances exist in the present water-ice model. We propos e a resonant mechanism for ice-breaking. It is based on destabilizing the f loating ice layer by applying localized harmonic perturbations, with a mode rate amplitude and at a resonant frequency.