Transformation of the First Mode Breather of Internal Waves above a Bottom Step in a Three-Layer Fluid

Abstract

We consider the problem of the propagation of a localized internal perturbation in the form of an oscillating wave packet (breather) of the first mode in a three-layer fluid with an uneven bottom in the form of a smooth step. The study is carried out using a method of numerical simulation within a fully nonlinear two-dimensional (in the vertical plane) set of Navier–Stokes equations. A set of calculations has been performed for different widths and heights of the bottom step. Inhomogeneity of the medium leads to the transformation of the internal wave field with the formation of weak reflected waves of the lowest modes and one or two first-mode breathers that propagate to the region of shallower depths. It is found from the analysis of linear stability in the terms of Richardson and Froude numbers that potentially unstable regions appear at the smallest values of the step width. An amplitude and energy analysis of secondary reflected nonlinear waves has been performed. The vertical mode composition of the fully nonlinear wave field has been analyzed. It is shown that the first mode makes the largest contribution to the vertical structure of the full-nonlinear packet, though the fourth, second, and third modes also make a noticeable contribution.