Chapman, S. J. and VandenBroeck, J. (2002) Exponential asymptotics and capillary waves. SIAM Journal on Applied Mathematics, 62 (6). pp. 18721898. ISSN 1095712X

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Official URL: http://www.siam.org/journals/siap/626/38116.html
Abstract
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 rightangled 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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