Drift of elastic floating ice sheets by waves and current, part I: single sheet

Abstract

The drift motion of a freely floating deformable ice sheet in shallow water subjected to incident nonlinear waves and uniform current is studied by use of the Green–Naghdi theory for the fluid motion and the thin plate theory for an elastic sheet. The nonlinear wave- and current-induced forces are obtained by integrating the hydrodynamic pressure around the body. The oscillations and translational motion of the sheet are then determined by substituting the flow-induced forces into the equation of motion of the body. The resulting governing equations, boundary and matching conditions are solved in two dimensions with a finite difference technique. The surge and drift motions of the sheet are analysed in a broad range of body parameters and various wave-current conditions. It is demonstrated that wavelength to sheet length ratio plays an important role in the drift response of the floating sheet, while the sheet mass and rigidity have comparatively less impact. It is also observed that while the presence of the ambient current changes the drift speed significantly (almost linearly), it has little to no effect on its oscillations. However, under the same ambient current, the drift speed changes remarkably by the wave period (or wavelength).