Experimental Study of the Velocity Field in Solitary Water Waves

Abstract

We describe experiments that have been conducted to investigate the velocity field in a solitary water wave. The horizontal and vertical velocity components were measured. The experimental results show that the horizontal velocity component is monotonically increasing with the distance to the wave crest line but the vertical velocity is not monotonic.

Recovery of Stokes waves from velocity measurements on an axis of symmetry

“…[15]. Finally, we emphasize that the horizontal velocity on crest or trough lines has been measured in many laboratory experiments [18,21,22,29,31] and therefore we expect that the practical accuracy of our recovery method can be verified numerically.…”

“…The main tool used in our approach is a very recent observation pertaining to the regularity of rotational flows: any weak solution of the water wave problem possesses realanalytic streamlines, the radius of analyticity being independent of the position in the fluid, cf [15]. Finally, we emphasize that the horizontal velocity on crest or trough lines has been measured in many laboratory experiments [18,19,21,22,29,31] and therefore we expect that the practical accuracy of our recovery method can be verified numerically.…”