Transformation of first mode breather of internal waves above the bottom step in a three-layer fluid

Abstract

In the present study we consider 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 shaped as a smoothed step. The study is carried out by methods of numerical simulation within a fully nonlinear two-dimensional (vertical plane) set of NavierStokes equations. A set of calculations was carried out for different widths and heights of the bottom step. Inhomogeneity of the medium leads to transformation of the internal wave field with the formation of weak reflected waves and one or two first-mode breathers passed to the shallow zone. By analyzing linear stability in terms of Richardson and Froude numbers, it was revealed that potentially unstable regions arise at the smallest values of the step width. An amplitude and energy analysis of secondary reflected nonlinear waves was performed. The vertical mode composition of the fully nonlinear wave field is 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 the third modes also contribute noticeably.

Breather interactions in a three-layer fluid

“…Rouvinskaya et al (2015) investigated shoaling breathers and compared solutions of the Gardner equation, with an additional shoaling term, with fully nonlinear numerical simulations. Lobovikov et al (2019) also undertook numerical simulations to investigate the shoaling of internal wave breathers from a symmetric stratification in deep water to an asymmetric stratification in shallow water and found that two breathers could form in the shallow water if the step was large enough. Energy was also transferred to small-amplitude trailing waves and reflected waves.…”