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Computing unstable periodic waves at the interface of two inviscid fluids in uniform vertical flow


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Forbes, LK and Chen, MJ and Trenham, C (2007) Computing unstable periodic waves at the interface of two inviscid fluids in uniform vertical flow. Journal of Computational Physics, 221 (1). pp. 269-287. ISSN 0021-9991

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Periodic waves at the interface of two immiscible fluids are considered. Each fluid is inviscid and incompressible, and is
moving vertically with constant speed. The upper fluid is more dense than the lower one, and the interface between them is
thus unstable to small perturbations. A linearized solution, valid for waves of small amplitude, is reviewed and a novel
numerical method is presented for computing waves of moderate amplitude. The technique uses a Fourier–Galerkin
approach, and converts the governing equations into a system of ordinary differential equations for the Fourier coefficients.
It is then shown how the method may be modified to allow for the evolution of overhanging waves, using a novel
time-dependent arclength formulation.

Item Type: Article
Journal or Publication Title: Journal of Computational Physics
Publisher: Academic Press Inc Elsevier Science
Page Range: pp. 269-287
ISSN: 0021-9991
Identification Number - DOI: 10.1016/
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Date Deposited: 07 Apr 2008 14:38
Last Modified: 18 Nov 2014 03:35
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