Numerical investigation of the influence of various factors on the propagation and transformation of solitary waves in the sea

For various stratifications and different types of bottom patterns we study the transformations of solitary perturbations of density appearing in the depth of the sea. In the two-dimensional case, under the assumption that the average dynamic characteristics weakly vary in time as compared with the wave characteristics, we deduce the equations for mean currents and waves taking into account vertical and horizontal viscosity and the diffusion of density. Numerical examples show that the stratification, bottom topography, nonlinearity, mean currents, and dissipation strongly affect both the process of splitting of a solitary wave into wave trains and their amplitude and length. The wave currents exhibit the oscillatory (train-like) character. It is emphasized that, in the case of propagation of solitary perturbations of density with dissipation, it is also important to take into account the combined influence of nonlinearity, currents, bottom topography, and stratification. Translated by Peter V. Malyshev and Dmitry V. Malyshev