The dependence of wave damping below solid ice is investigated for the ice model with nonlinear visco-elastic rheology, taking into account existing data on the transient creep of ice. The nonlinear dispersion equation and modified nonlinear Schrodinger equation (NLS) are derived. The influence of the nonlinear visco-elastic rheology of ice and the eddy viscosity in the ice-adjacent water layer on wave damping and modulation instability are investigated and discussed in this paper.
Surface waves can propagate below drift ice and create ice failure over large distances in a relatively short time. These effects are important for sea ice dynamics and energy exchange between the atmosphere and the ocean. According to the data of the USSR Register on the wave climate in Russian Arctic seas (Smirnov, 1987), the typical periods of wind waves and swells are in the range of 7.6 to 14 s. Experimental data on the spectral composition of flexural-gravity waves in the Arctic were analyzed by Nagurny et al. (1994) and Wadhams et al. (1995) to show that a major portion of the wave energy corresponds to waves with periods greater than 16 s. Wadhams et al. (1995) supposed that the most intensive vibrations of the ice cover are forced by the low-frequency portion of the swell spectrum, which propagates across long distances under the ice.
The propagation of surface waves below drift ice is accompanied by additional processes of energy dissipation in comparison with surface waves propagating in the water with an ice-free surface. The difference is explained by the influence of friction at the ice-water interface on the energy dissipation, floes interaction and energy dissipation in the ice caused by its bending. The influence of the eddy viscosity on wave damping below a continuous ice cover was discussed by Liu and Mollo-Christinsen (1987). They derived the temporal decay and spatial rates of monochromatic plane waves propagating in water of infinite depth covered by an elastic ice sheet and demonstrated that the results of the damping rate compared reasonably well with observations in the marginal ice zone (Wadhams, 1978; Weber, 1987).