Transformation of a fully nonlinear breather-like package of internal waves over a bottom step in a layered fluid

Abstract

In this paper, we study the process of transformation of a localized wave packet over a bottom step in a three-layer fluid, in which the height of the step is equal to or exceeds the thickness of the lower layer; therefore, density stratification becomes two-layer in the shallow water zone. In numerical experiments, both the height of the step and the width of the step were varied. The problem is solved in the framework of a fully nonlinear model of hydrodynamics of an inviscid incompressible stratified fluid. The primary analysis consisted in estimating the values of dimensionless parameters used, as a rule, in runup problems: the Froude and Iribarren numbers, the ratio of the characteristic wavelength to the characteristic slope width, the ratio of the topographic slope to the characteristic wave beam angle. Since the “cutoff” line for the lower pycnocline is partially or completely located on a step, one could expect the effects of run-up, breaking or reflection of waves propagating along the lower pycnocline, but this doesn’t happen. It is shown that the reflection of the wave packet from the step is minimal in all cases considered, a strong steepening of the wave is observed, but no breaking occurs in this case — the wave then just quickly decays on the lower pycnocline. An analysis of the spectral amplitudes and energy fields allows us to conclude that there is a transfer of energy from the lower pycnocline to the upper one. The breather in a two-layer fluid cannot exist, but the wave packet formed in the upper pycnocline after its destruction has much higher energy than it has before the step.