Solition models of long internal waves

Part of the Lecture Notes in Physics book series (LNP, volume 189)


The Korteweg-de Vries (KdV) equation and the finite-depth equation of Joseph (1977) and Kubota, Ko & Dobbs (1978) both describe the evolution of long internal waves of small but finite amplitude, propagating in one direction. In this paper, theories are tested experimentally by comparing measured and theoretical soliton shapes. The KdV equation predicts the shapes of our measured solitons with remarkable accuracy, much better than does the finite-depth equation. When carried to second-order, the finite-depth theory becomes about as accurate as (first-order) KdV theory for our experiments. However, second-order corrections to the finite-depth theory also identify a bound on the range of validity of that entire expansion. This range turns out to be rather small; it includes only about half of the experiments reported by Koop & Butler (1981).


Surface Wave Internal Wave Velocity Potential Boussinesq Approximation Integral Length Scale 
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© Springer-Verlag 1983

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