EXPONENTIAL NEUTRAL STABILITY OF A FLOATING ICE LAYER

Linear stability of two-dimensional monochromatic waves, i. e., normal modes, in a homogeneous elastic ice layer of finite thickness and inf inite horizontal extension floating on the surface of a water layer of finite depth is treated analytically. The water is assumed to be comp ressible but the viscous effects are neglected in the model. The treat ment is an extension of the two-step analysis in Brevdo [4] for a homo geneous waveguide overlaying a rigid half space. First, we apply an en ergy-type method and show that, for real wavenumbers k, omega(2) is re al, where omega is a frequency. Fur ther, to exclude purely imaginary Frequencies for real k, omega(2) use the dispersion relation function of the problem D(k, omega) and show that for omega = is, s is an eleme nt of R+, the equation D(k, is) = 0 does not have real roots in k. Hen ce, due to the symmetry, all normal modes in this model are neutrally stable. This result on the one hand provides a theoretical support for the physical relevance of the model and on the other hand points to a possibility of resonant algebraically growing responses to localized harmonic in time perturbations. It is also shown that an unstable vert ically stratified ice layer is always absolutely unstable. Based on th is result, a conjecture is made concerning a possible mechanism of spo ntaneous ice breaking as a consequence of emergence of absolute instab ility, which is caused by a weather induced appearance of an unstable ice stratification.