Long Internal Waves of Moderate Amplitudes. I. Solitons.
AERONAUTICAL RESEARCH ASSOCIATES OF PRINCETON INC NJ
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The Korteweg-deVries KdV equation and the finite-depth equation of Joseph 1977 and Kubota, Ko and Dobbs 1978 both describe the evolution of long internal waves of small but finite amplitude, propagating in one direction. In this paper, both 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 and Butler 1981. Author
- Numerical Mathematics
- Fluid Mechanics