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Second-order sloshing over an arbitrary bed

Second-order sloshing over an arbitrary bed

Authors :
G. J. D. Chapman
Richard Porter
Source :
Journal of Fluid Mechanics. 524:331-355
Publication Year :
2005
Publisher :
Cambridge University Press (CUP), 2005.

Abstract

The two-dimensional problem of the free sloshing of an inviscid fluid in a vertically walled tank with an arbitrary bed shape is solved at both first and second order in the Stokes expansion of the velocity potential. The approach employed at both orders uses Green's functions for a flat bed in conjunction with the Cauchy–Riemann equations to derive integral equations for the tangential flux along the varying bed. The first- and second-order potentials everywhere in the fluid may then be related to these fluxes. Significant analytic progress is made with the calculation of various contributions to the integral equations at second order. The equations at first and second order are ultimately solved using a variational principle equivalent to the Galerkin method, giving efficient and accurate results. In particular, the work involved in determining the second-order solution is no more intensive than in solving the first-order problem. The first-order solution is shown to reproduce known results for specific bed shapes. The method is applied to a range of bed shapes and the second-order correction to the free-surface elevation is illustrated.

Details

ISSN :
14697645 and 00221120
Volume :
524
Database :
OpenAIRE
Journal :
Journal of Fluid Mechanics
Accession number :
edsair.doi...........555fc5ac04553dc13bfb8731cdcd1b6c
Full Text :
https://doi.org/10.1017/s0022112004002502