Short wave phase shifts by large free surface solitary waves. Experiments and models

Overview & Synopsis

In this paper, we compare experiments on short gravity wave phase shifting by surface solitary waves to a Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) refraction theory. Both weak interactions (head-on interaction) and strong interactions (overtaking interaction) are examined. We derive a dispersion relation and wave action conservation relation which are similar to the ones obtained for short waves refraction on slowly varying media. The model requires an exact solitary wave solution. To this end, a steady wave solution is numerically computed using the algorithm devised by Byatt-Smith [Proc. R. Soc. London, Ser. A 315, 405 (1970)]. However, two other solitary wave solutions are incorporated in the model, namely the classical Korteweg and De Vries (KdV) [Phil. Mag. 39, 422 (1895)] solution (weakly nonlinear/small amplitude solitary wave) and the Rayleigh [Phil. Mag. 1, 257 (1876)] solution (strongly nonlinear/large amplitude solitary wave). Measurements of the short wave phase shift show better agreement with the theoretical predictions based on the Byatt-Smith numerical solution and the Rayleigh solution rather than the Korteweg and De Vries one for large amplitude solitary waves. Theoretical phase shifts predictions based on Rayleigh and Byatt-Smith numerical solutions agree with the experiments for A/h0⩽0.5. A new heuristic formula for the phase shift allowing for large amplitude solitary waves is proposed as a limiting case when the short wave wave number increases.