Shoaling of an Internal Wave Packet in an almost Three-Layer Sea over a Steep Shelf

L. V. Talalushkina, O. E. Kurkina, A. A. Kurkin*, A. R. Giniyatullin

Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia

*e-mail: aakurkin@gmail.com

Abstract

The paper considers in detail propagation and transformation of a localized internal wave packet over an irregular bottom in the form of a step in a three-layer liquid in the framework of a model based on the Gardner equation. This situation is typical for a stratified sea shelf, where groups of short-period waves generated by a barotropic tide propagate from the deep sea to the shallow water. As a boundary condition on the outer boundary of the “shelf”, an exact one-breather solution of a homogeneous problem is used, which then changes in a horizontally inhomogeneous medium. A series of numerical experiments for different ledge heights and breather (nonlinear localized oscillating wave packet with a soliton-like envelope) parameters is carried out. Three qualitatively different transformation scenarios are identified: a) “adjustment” of the wave packet that conserves its structure, but changes the amplitude and length of its constituent waves; b) transformation of the wave packet into two solitary waves (crest and trough); с) decay of the wave packet into dispersing quasilinear wave trains. The analysis of the flow velocity field induced by the propagation of the wave packet is performed. Due to the bottom current structure here, zones of multidirectional flows alternate along the horizontal coordinate forming zones of divergent and convergent currents, respectively. The distributions of the exceedance probabilities for the velocities of these flows along the horizontal axis are almost symmetric and periodic in case a), substantially asymmetric in case b), and are irregular and inhomogeneous in case c). It is shown that zones of intense currents with sharp inhomogeneities can appear with strong gradients of the internal wave fields, where their influence on the environment increases.

Keywords

horizontally inhomogeneous ocean, breather, wave packet, three-layer density stratification, Gardner equation, bottom step, wave transformation

Acknowledgments

The presented results were obtained within the framework of the state assignment in the field of scientific activity (project No. FSWE-2020-0007) and with the financial support of the grant of the President of the Russian Federation for state support of Candidates of Sciences MK-218.2020.5.

For citation

Talalushkina, L.V., Kurkina, O.E., Kurkin, A.A. and Giniyatullin, A.R., 2021. Shoaling of an Internal Wave Packet in an Almost Three-Layer Sea over a Steep Shelf. Ecological Safety of Coastal and Shelf Zones of Sea, (4), pp. 5–26. doi:10.22449/2413-5577-2021-4-5-26 (in Russian).

DOI

10.22449/2413-5577-2021-4-5-26

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