Is linear hydrodynamics sufficient to predict breaking lengths correctly?

Abstract

The bending failure of level ice in 2D is mainly characterized by its breaking length and interaction forces. In this paper a study is carried out to assert if a 2D ice-structure interaction model based on an incompressible, inviscid and irrotational fluid together with the linearized Bernoulli equation for ice can reproduce the dependence of the breaking length on the interaction velocity as observed in experiments. To this end a 2D model is composed in which the ice, modelled as a semi-infinite Euler-Bernoulli beam, is pushed into a rigid, immovable, downward-sloping structure with a fixed horizontal velocity. The beam rests on the finite depth, infinitely wide fluid layer. To assert whether this linear description of the fluid suffices, the velocity dependence of the breaking length predicted by this model is compared with the experimentally validated 2D model of (Valanto 1992). The comparison shows that linear hydrodynamics gives significant error in certain velocity ranges. Recommendations are given as to a fluid model that would result in an improved prediction of the velocity dependence of the breaking length.