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SIAMAM
2002

Exponential Asymptotics and Capillary Waves

13 years 10 months ago
Exponential Asymptotics and Capillary Waves
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. Key words. exponentially small, Stokes lines, optimal truncation, divergent expansions, singular perturbation, surface tension AMS subject classifications. 76B07, 76B45, 41A60, 35B25 PII. S003613990038116X
Jean-Marc Vanden-Broeck, S. Jonathan Chapman
Added 23 Dec 2010
Updated 23 Dec 2010
Type Journal
Year 2002
Where SIAMAM
Authors Jean-Marc Vanden-Broeck, S. Jonathan Chapman
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