Compressible effects in the propagation of nonlinear shallow water waves: Models and simulations

Zuccoli, Emanuele and Kadri, Usama ORCID: https://orcid.org/0000-0002-5441-1812 2025. Compressible effects in the propagation of nonlinear shallow water waves: Models and simulations. European Journal of Mechanics - B/Fluids 116 , 204397. 10.1016/j.euromechflu.2025.204397

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Abstract

We investigate the effects of compressibility in the propagation of shallow-water waves and extend the classical shallow-water equations to a compressible regime. Both non-dispersive and weakly-dispersive nonlinear waves are then analysed with the help of the multiple scales method, ultimately leading to the studying of a Burgers and a Korteweg–deVries equation, respectively. A parametric study is conducted in order to investigate the interplay of both nonlinearity and compressibility and assess how compressibility may alter the nonlinear properties of the waves. In particular, parameters varied are the compressibility coefficient , the amplitude of the waves and the width of the initial wave profile . In a non-dispersive regime, shock and rarefaction waves form and interact one another leading to a progressive reduction of the wave amplitude in time. The compressibility of the fluid speeds up the shock formation, with beneficial effects in terms of wave amplitude reduction. In a weakly dispersive regime, on the other hand, higher compressibility values may amplify the initial perturbation, leading to the formation of a discrete number of solitons having amplitudes much greater than the amplitude at the initial stage. The analysis presented in this work aims at improving our predictions on the dynamics of nonlinear compressible shallow-water waves both in terms of wave amplitude variation and propagation time. Among various applications, our enhanced models can notably improve the estimation of tsunami arrival times and contribute to more accurate weather forecasts. Furthermore, the work presented here lays the foundation for future experimental studies and assessments in this field.

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	Elsevier
ISSN:	0997-7546
Date of First Compliant Deposit:	31 October 2025
Date of Acceptance:	18 October 2025
Last Modified:	31 Oct 2025 12:00
URI:	https://orca.cardiff.ac.uk/id/eprint/182018

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