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I don't know hydrodynamics, but I wonder how one would compute resonance modes of a cubic box of water which we shake. I believe the waves would directly depend on the height of water and the width and length of the box. Is it a bit like a waveguide for electodynamics?

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up vote 5 down vote accepted

Yes it is a bit like waveguide for electrodynamics. You've got absolutely the same equation. The difference is in boundary conditions -- instead of Dirichlet you've got to use Neumann boundary conditions.

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While of course it works only if you are able no neglect all the non-linear effects -- your waves are low enough.

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For the smaller wavelengths surface tension also comes into play. – Omega Centauri Jan 31 '11 at 16:34
Well, yes. But you still can linearise this. – Kostya Jan 31 '11 at 16:42
Kosttya, yes you can. The main effect will be that the frequencies versus wavelength plot will have different slopes at short versus long wavelengths. – Omega Centauri Jan 31 '11 at 19:20
Well, of course. But it is irrelevant to my discussion. We are dealing with Laplace equation -- check the reference. There is no time and therefore no frequencies. – Kostya Jan 31 '11 at 20:09

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