A Scaling Law for the Flexural Motion of Floating Ice

Abstract

This paper presents a mathematical study of flexural motion of floating ice, including hydrodynamic effects, to derive a scaling law by reducing the deep-water dispersion equation to scale-independent form. The scaling shows that the well-known characteristic length, ${l_c} = \sqrt[4]{{D/\rho g}}$ and less well known characteristic time, ${t_c} = \sqrt {{l_c}/g}$ , are unique in reducing solutions to canonical, scale-independent, form. The canonical solutions show that flexural motion is quasi-static for periods much greater than 2πtc , and is dynamic for shorter periods, with significant propagating waves. These conclusions are largely independent of the geometry of the ice sheet under consideration, the surrounding ice/water conditions, or distribution of applied forcing.