, Volume 207, Issue 3, pp 907-917

Mean Velocities in a Stokes Wave

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We prove that in a periodic travelling wave propagating at the surface of an inviscid homogenous fluid in irrotational flow over a flat bed, the horizontal mean velocity exceeds the depth-averaged velocity in the frame of reference in which the wave is stationary. The long-standing conjectural nature of this fundamental issue was due to its undecidability within the framework of linear wave theory.

Communicated by C. Dafermos