Breaking Ice with Gravity Waves

The plane-wave impulse response of a laterally compressed floating elastic plate, derived in earlier work, provides a simple means of describing the response of a floating ice sheet to gravity waves induced by a moving vehicle. Vehicle speeds above the cut-off phase velocity produce gravity waves that grow in amplitude with time. These waves grow in amplitude most rapidly when the vehicle speed equals the critical gravity-wave phase velocity. For vehicle speeds above the critical phase velocity, the critical wave is excited at an angle to the vehicle motion; hence, the amplitude grows at a high but decreasing rate as the vehicle speed increases from the critical speed. The critical speed is the optimum speed for breaking an ice sheet by moving vehicle. Vehicles travelling at speeds below the cut-off phase velocity do not excite growing waves that increase the deflection of the ice sheet; thus, vehicular travel below the cut-off speed is recommended. Easily derived plots of the cut-off and critical phase velocities and wave lengths are presented as functions of ice thickness and water depth.