Abstract: We propose a system of first-order balance laws that describe the propagation of internal solitary waves in a multilayer stratified shallow water with non-hydrostatic pressure in the upper and lower layers. The construction of this model is based on the use of additional variables, which make it possible to approximate the Green–Naghdi-type dispersive equations by a first-order system. In the Boussinesq approximation, the governing equations allow one to simulate the propagation of non-linear internal waves, taking into account fine density stratification, a weak velocity shear in the layers, and uneven topography. We obtain smooth steady-state soliton-like solutions of the proposed model in the form of symmetric and non-symmetric waves of mode-2 adjoining to a given multilayer constant flow. Numerical calculations of the generation and propagation of large-amplitude internal waves are carried out using both the proposed first-order system and Green–Naghditype equations. It is established that the solutions of these models practically coincide. The advantage of the first-order equations is the simplicity of numerical implementation and a significant reduction in the calculation time. We show that the results of numerical simulation are in good agreement with the experimental data on the evolution of mode-2 solitary waves in tanks of constant and variable height 01 December 2023 05:32:

Cite: А. А. Чесноков , V. E. Ermishina , V. Yu. Liapidevskii
Strongly non-linear Boussinesq-type model of the dynamics of internal solitary waves propagating in a multilayer stratified fluid
Physics of Fluids. 2023. V.35. N7. 076605 :1-13. DOI: 10.1063/5.0151928 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Mar 26, 2023
Accepted:	Jun 23, 2023
Published print:	Jul 10, 2023

Identifiers:

Web of science:	WOS:001026250700003
Scopus:	2-s2.0-85164953865
Elibrary:	61785763
OpenAlex:	W4383816988

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OpenAlex	2
Elibrary	3
Scopus	2
Web of science	2

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