Multi-modal destabilization of a floating ice layer by wind stress

In this paper, we study a destabilization by wind stress of a homogeneous e lastic ice layer of infinite extent and finite thickness floating on a wate r layer of finite depth. The water is assumed to be compressible; the visco us dissipation is neglected in both the ice and the water layers. Two model s are considered. In the first one, the ice layer is compressed by a wind s tress acting far away from the region of consideration. This model was foun d to have similar stability properties as a model where the ice layer is as sumed to be thin. The destabilization occurs for values of compression that are greater than the maximum admissible value above which ice can no longe r be treated as an elastic material. In the second model, the compression w as fixed below the maximum admissible value and a homogeneous wind shear st ress was applied to the upper surface of the ice laver. In this model, the entire infinite set of frequency branches was found to be destabilized for wind shear stresses well within the range relevant for observable condition s. For long waves, the most unstable mode is the buckling mode; for short w aves, the most unstable mode is the acoustic mode; and in the intermediate range a high-order L seismic mode is the most unstable. The buckling mode i s well approximated by the buckling mode in the thin plate model. The phase velocities of all the unstable normal modes on the most unstable branches, and the group velocity of the unstable wave packet of the buckling mode al l point in the direction opposite to the direction of wind action. The loca lized unstable disturbances that are related to the buckling mode propagate against the wind. (C) 2001 Elsevier Science BN. All rights reserved.