Wave drag during an unsteady motion

The average wave drag in unsteady motion is studied experimentally with force measurements. Towing hulls of size L at sinusoidal speed, the mean drag is measured for different amplitudes and frequencies of the fluctuating velocity, as well as different Froude numbers F₀ associated with the mean velocity V₀ ( F₀ = V₀/√gL ). The wave drag is reported to be either increased or decreased by velocity fluctuations depending on F₀ . For small fluctuation amplitudes, this drag change is proportional to the square of the amplitude. The effect is maximized for a resonance frequency identified as the Wehausen frequency, which scales as √g/L times the inverse of the Froude number. All these results are rationalized by developing an extension to Havelock's theory.