“…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.…”