Long‐period gravity waves in ice‐covered sea

Abstract

A floating ice sheet under compressive stress is modeled as a laterally compressed thin linearly elastic plate, floating on a compressible liquid of constant depth over a rigid bottom. This system is analyzed as a wave guide for plane waves. Sinusoidal traveling waves having vertical planes of constant phase are sought for the impulse response of the system. Two bands of gravity waves are found: (1) flexural and (2) floating‐membrane. The two bands join at the critical frequency of the system, at which the impulse response is unbounded. The long‐period floating‐membrane gravity waves exist at all frequencies below the flexural gravity wave band. For long‐period gravity waves the coupling force between plate and liquid is found to be a Hooke's Law force; the effective foundation modulus is directly proportional to the difference between the square of the phase velocity of a wave in the floating‐plate system and that of a free‐surface gravity wave at the same wavelength. The analogy of an elastic plate supported on an elastic foundation is apt for these long‐period waves. It is concluded that the impulsive release of stored elastic energy when the compressed ice breaks supplies adequate energy to produce measurable long‐period waves in floating ice. The results suggest that long‐period wave motion accompanies lateral compression of the ice sheet; hence wave measurements may provide a means of detecting the buildup of widespread compressive stress in the ice.