Stability analysis and solitary waves on Plateau border flows

Walpole, Benjamin and Parau, Emilian (2025) Stability analysis and solitary waves on Plateau border flows. Journal of Fluid Mechanics. ISSN 0022-1120 (In Press)

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Abstract

We investigate the linear stability of a Plateau border and the existence of solitary waves. Firstly, we formulate a new non-orthogonal coordinate system that describes the specific geometry of a Plateau border. Within the framework of this coordinate system, the equations of motion for the fluid potential and free surface are derived. By performing a linear stability analysis we find that the Plateau border is stable under small perturbations. Next, a weakly nonlinear theory is developed, leading to a Korteweg-de Vries equation for the free surface profile. Our weakly nonlinear evolution equation predicts depression solitary waves, such as those observed by (Bouret et al. 2016).

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Engineering, Mathematics and Physics
UEA Research Groups:	Faculty of Science > Research Groups > Fluids & Structures
Depositing User:	LivePure Connector
Date Deposited:	15 Dec 2025 11:30
Last Modified:	15 Dec 2025 11:30
URI:	https://ueaeprints.uea.ac.uk/id/eprint/101390
DOI:	issn:0022-1120

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