Mathematical simulation of gravitational waves in the ocean in the approximation of “shallow water”

Abstract

Problems of the behavior of gravitational waves in the approximation of “shallow water” — motion of a solitary wave over the water surface, exit of a wave to the shore, passage of a solitary wave over a submerged rock — are solved. The solution of the first problem showed that in modeling the motion of a solitary (soliton-type) wave the “shallow water” approximation breaks down at a ratio of water depth to wavelength equal to 0.3. An analysis of the results of solution of the second problem indicates that the “shallow water” approximation cannot be used for calculation of the height of a wave in its exit to the shore but it can be used for estimation of the distance from the shore where the wave is turned over. It follows from the solution of the third problem that the “shallow water” approximation is suited only for obtaining a qualitative picture of the distortion of the profile of a wave in its motion over a rock.