Higher order corrections for shallow-water solitary waves: elementary derivation and experiments

Details Higher order corrections for shallow-water solitary waves: elementary derivation and experiments Higher order corrections for shallow-water solitary waves: elementary derivation and experiments

2009-03-25

arxiv.org/abs/0903.4272v2

European Journal of Physics, Vol. 30, 1311-1323 (2009)

Physics

Fluid Dynamics

15 pages, 8 EPS figures, uses IOP class file for LaTeX2e, slightly revised version

Scientific paper

10.1088/0143-0807/30/6/009

We present an elementary method to obtain the equations of the shallow-water solitary waves in different orders of approximation. The first two of these equations are solved to get the shapes and propagation velocities of the corresponding solitary waves. The first-order equation is shown to be equivalent to the Korteweg-de Vries (KdV) equation, while the second-order equation is solved numerically. The propagation velocity found for the solitary waves of the second-order equation coincides with a known expression, but it is obtained in a simpler way. By measuring the propagation velocity of solitary waves in the laboratory, we demonstrate that the second-order theory gives a considerably improved fit to experimental results.

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