On the critical free-surface flow over localised topography

Keeler, J. S. ORCID: https://orcid.org/0000-0002-8653-7970, Binder, B. J. and Blyth, M. G. (2017) On the critical free-surface flow over localised topography. Journal of Fluid Mechanics, 832. pp. 73-96. ISSN 0022-1120

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Abstract

Flow over bottom topography at critical Froude number is examined with a focus on steady, forced solitary wave solutions with algebraic decay in the far-field, and their stability. Using the forced Korteweg-de Vries (fKdV) equation the weakly-nonlinear steady solution space is examined in detail for the particular case of a Gaussian dip using a combination of asymptotic analysis and numerical computations. Non-uniqueness is established and a seemingly infinite set of steady solutions is uncovered. Non-uniqueness is also demonstrated for the fully nonlinear problem via boundary-integral calculations. It is shown analytically that critical flow solutions have algebraic decay in the far-field both for the fKdV equation and for the fully nonlinear problem and, moreover, that the leading-order form of the decay is the same in both cases. The linear stability of the steady fKdV solutions is examined via eigenvalue computations and by a numerical study of the initial value fKdV problem. It is shown that there exists a linearly stable steady solution in which the deflection from the otherwise uniform surface level is everywhere negative.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Fluid and Solid Mechanics
Depositing User:	Pure Connector
Date Deposited:	01 Sep 2017 05:08
Last Modified:	22 Oct 2022 03:06
URI:	https://ueaeprints.uea.ac.uk/id/eprint/64716
DOI:	10.1017/jfm.2017.639

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