Resonant destabilization of a floating homogeneous ice layer

  • L. Brevdo


We show that a homogeneous elastic ice layer of finite thickness and infinite horizontal extension floating on the surface of a homogeneous water layer of finite depth possesses a countable unbounded set of of resonant frequencies. The water is assumed to be compressible, the viscous effects are neglected in the model. Responses of this water-ice system to spatially localized harmonic in time perturbations with the resonant frequencies grow at least as \(\sqrt{t}\) in the two-dimensional (2-D) case and at least as lnt in the three-dimensional (3-D) case, when time \(t\to\infty.\) The analysis is based on treating the 3-D linear stability problem by applying the Laplace-Fourier transform and reducing the consideration to the 2-D case. The dispersion relation for the 2-D problem \({D}(k,\omega) = 0,\) obtained previously by Brevdo and Il'ichev [10], is treated analytically and also computed numerically. Here k 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 set of roots \((k, \omega) = (0,\omega_n), n\in\Bbb Z\) with \(\rm{Im}\ \omega_n = 0.\) Then the analysis of Brevdo [6], [7], [8], [9], which showed the existence of resonances in a homogeneous elastic waveguide, is applied to show that similar resonances exist in the present water-ice model. We propose a resonant mechanism for ice-breaking. It is based on destabilizing the floating ice layer by applying localized harmonic perturbations, with a moderate amplitude and at a resonant frequency.

Key words. Floating ice layer, resonant frequencies, destabilization, logarithmic growth, resonant ice-breaking mechanism. 


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Copyright information

© Birkhäuser Verlag, Basel, 2001

Authors and Affiliations

  • L. Brevdo
    • 1
  1. 1.Ecole Supérieure de Mécanique de Marseille, Université de la Méditerranée, IMT - Technopôle de Château-Gombert, F-13451 Marseille Cedex 20, France e-mail: brevdo@esm2.imt-mrs.frFR

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