The Mathematical Institute, University of Oxford, Eprints Archive

Exponential asymptotics and capillary waves

Chapman, S. J. and Vanden-Broeck, J. (2002) Exponential asymptotics and capillary waves. SIAM Journal on Applied Mathematics, 62 (6). pp. 1872-1898. ISSN 1095-712X


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Recently developed techniques in exponential asymptotics beyond all orders are employed on the problem of potential flows with a free surface and small surface tension, in the absence of gravity. Exponentially small capillary waves are found to be generated on the free surface where the equipotentials from singularities in the flow (for example, stagnation points and corners) meet it. The amplitude of these waves is determined, and the implications are considered for many quite general flows. The asymptotic results are compared to numerical simulations of the full problem for flow over a polygonal plough and for flow round a right-angled corner, and they show remarkably good agreement, even for quite large values of the surface tension parameter.

Item Type:Article
Uncontrolled Keywords:exponentially small; Stokes lines; optimal truncation; divergent expansions; singular perturbation; surface tension
Subjects:O - Z > Partial differential equations
D - G > Fluid mechanics
Research Groups:Oxford Centre for Industrial and Applied Mathematics
ID Code:607
Deposited By: Jon Chapman
Deposited On:24 May 2007
Last Modified:29 May 2015 18:25

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