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arXiv · 2401.12411

Oscillatory and regularized shock waves for a modified Serre-Green-Naghdi system

Daria Bolbot·Dimitrios Mitsotakis·Athanasios E. Tzavaras
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Abstract

The Serre-Green-Naghdi equations of water wave theory have been widely employed to study undular bores. In this study, we introduce a modified Serre-Green-Naghdi system incorporating the effect of an artificial term that results in dispersive and dissipative dynamics. We show that, over sufficiently extended time intervals, effectively approximates the classical Serre-Green-Naghdi equations and admits dispersive-diffusive shock waves as traveling wave solutions. The traveling waves converge to the entropic shock wave solution of the shallow water equations when the dispersion and diffusion approach zero in a moderate dispersion regime. These findings contribute to an understanding of the formation of dispersive shock waves in the classical Serre-Green-Naghdi equations and the effects of diffusion in the generation and propagation of undular bores.

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Daria Bolbot, Dimitrios Mitsotakis, Athanasios E. Tzavaras. 2024-01-22. Oscillatory and regularized shock waves for a modified Serre-Green-Naghdi system. https://arxiv.org/abs/2401.12411

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