Resonances and wave instabilities in the shallow water limit

instabilitiesThe talk of Takeshi Kataoka, on Tuesday 29 July, started with a review of the resonance curves in finite depth and moderately shallow water, from the paper of McLean (1982).  The finite-amplitude instabilities are generally close to these curves.   However, in shallow water they can depart.  He next reviewed results on instabilities in shallow water by Francius & Kharif (2006), where new instabilities in shallow water were discovered.  He then introduced new results, by first introducing new resonance curves in shallow water.  These resonance curves are straight lines in the perturbation wavenumber (p,q) space.  For very shallow water, matched asymptotic expansions were used to separate an inner and outer region.  Comparison with numerics showed that the finite-amplitude instabilities more closely followed the new shallow water resonance curves. A video of the talk is available here.

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