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The classical Benjamin and Lighthill conjecture about steady water wavesstates that the non-dimensional flow force constant of a solution is bounded bythe corresponding constants of the supercritical and subcritical uniformstreams respectively. These inequalities determine a parameter region thatcovers all steady motions. In fact not all points of the region determine asteady wave. In this note we prove a new and explicit lower bound for the flowforce constant, which is asymptotically sharp in a certain sense. Inparticular, this recovers the well known inequality F<2 for the Froude number,while significantly reducing the parameter region supporting steady waves.

Improved bound in the Benjamin and Lighthill conjecture