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Uni-modal destabilization of a viscoelastic floating ice layer by wind stress. (English) Zbl 1103.74025
Summary: We study a destabilization by wind stress of a homogeneous viscoelastic ice layer of infinite horizontal extent and finite thickness floating on a water layer of finite depth. The water is assumed to be weakly compressible; the viscous dissipation in the water layer is shown to be negligible compared to that in the ice layer. In the model, we assume that a homogeneous wind shear stress is applied to the upper surface of the ice layer at near field, and the compression within the ice layer is fixed below the maximum admissible value, i.e. below the value above which ice can no longer be treated as an elastic material. The effect of viscosity is shown to stabilize the acoustic mode and all the unstable seismic modes that in a purely elastic model, treated by L. Brevdo and A. Il’ichev [Cold Reg. Sci. Technol. 33, 77–89 (2001)], possess unbounded growth rates for a growing wave number. The buckling mode is unstable in the domain of parameters considered. In all the cases treated, the model is marginally absolutely stable. The localized unstable disturbances propagate against the wind. The spatially amplifying waves in the model amplify in the direction opposite to the wind direction. The stability results are well approximated by those for a Kirchoff–Love thin ice plate model.

MSC:
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
74D05 Linear constitutive equations for materials with memory
74H55 Stability of dynamical problems in solid mechanics
86A40 Glaciology
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