Inertial motion of a circular cylinder approaching obliquely an ice cover.

Two-dimensional unsteady problem of an inertial motion of a circular cylinder approaching obliquely an ice cover and the response of ice to this motion are investigated. The liquid under the ice is inviscid, incompressible and of infinite depth. The ice sheet floating on water surface is modelled as a thin elastic plate of constant thickness and of infinite extent. The movement of the cylinder is governed by its inertia, gravity, hydrodynamic force, deflection of the ice cover and the initial conditions. The general coupled problem is approximately decoupled for relatively small speeds of the body. Within the decoupled approach, the cylinder motion, the generated flow, and the hydrodynamic pressure in the fluid are determined by conformal mapping method without account for the ice deflection. The obtained hydrodynamic loads are applied to the equation of elastic ice sheet, and the ice deflection, speed of deflection and strains in the ice are evaluated by Fourier transform method. The oblique inertial motion of a circular cylinder under the rigid plate is described analytically. A critical Froude number for a heavy cylinder, which is only dependent on the initial submergence depth, is introduced and used in classification of the body motions. The present study is focused on the motions of circular cylinders without their impacts with the plate. It is shown that the ice can be damaged even before the cylinder arrives at the position closest to the plate. For a given radius of the cylinder and its initial kinetic energy, the conditions of the motion including the angle of attack and the dimensionless submergence depth which lead to ice breaking are predicted.