Capillary waves understood by an elementary method |
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| Authors: | Kern E Kenyon |
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| Institution: | (1) 4632 North Lane, 92014-4134 Del Mar, CA, U.S.A. |
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| Abstract: | The central physics of capillary waves (or ripples) can be understood by an elementary method which makes use of the balance
of static and dynamic pressure differences along the surface streamline between crest and trough, in the steady reference
frame, and conservation of mass through vertical cross-sections beneath crest and trough. Basically Einstein’s (1916) model
of surface gravity waves is adapted for the purpose of explaining the existence of capillary waves of infinitesimal amplitude.
One product of the physical understanding, the phase speed of capillary waves, is derived as a function of the wave length
and surface tension and the result agrees exactly with that obtained by the classical mathematical procedure. In the elementary
method it is not necessary to assume irrotational flow, upon which the classical theory is founded, nor are perturbation expansions
of the nonlinear fluid equations employed. The extension to capillary-gravity waves, by including the acceleration of gravity
in the physical model, is straightforward, and the calculated phase speed of these waves is identical to what is found in
the text books as well. |
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| Keywords: | Capillary waves ripples |
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