Wave drag in unsteady motion*

Objects moving at the surface of water thanks to a cyclic propulsion often travel at a constantly changing velocity. This talk focuses on the consequence of such unsteadiness on the wave resistance.

The average wave drag in unsteady motion is studied experimentally with force measurements, and described by an extended version of Havelock's theory. Towing hulls of size L at sinusoidal speed, the mean drag is measured for different amplitudes, frequencies of the fluctuating velocity, as well as different Froude numbers associated with the mean velocity (Fr=U/√(gL) ).

Depending on the Froude number, the wave drag is either increased or decreased by velocity fluctuations and depends linearly on the square of their amplitude. The effect is maximum for a resonance frequency identified as the Wehausen frequency, scaling like the inverse of the Froude number Ω ∝ 1/Fr. These results are rationalized on the basis of a theoretical framework for the unsteady wave drag.