Excitation of tsunami waves by a traveling displacement of the ocean bottom

Abstract

The problems of wave excitation in the ocean by a vertical displacement occurring in a rectangular region of the bottom and traveling along this region with the arbitrary velocity are considered. The analysis is made in the framework of the linear theory of long waves, which correspond well, in general, to tsunami waves in the open ocean. Two models of displacement are discussed: (1) rectangular, and (2) sign‐variable in the direction transverse to its propagation. The main characteristics of radiated waves (the form and amplitude of impulses, the direction dependence of the wave energy, the dependence of the full energy of radiation E on duration T and the propagation velocity V of the break) are calculated. In all cases E grows with the approximation of V to the velocity of long waves (synchronism), the radiation having a sharp directivity. Generally speaking the second‐type displacement radiates the waves less effectively than the first one, except for the case of synchronism, however. In the longitudinal case V → ∞ the results obtained for the first type displacements coincide with the solutions found earlier by Kajiura.