Lord Kelvin saved from the waters !

In 1887 Lord Kelvin showed that the wake created by a ship moving at a uniform pace is always delimited by an angle equal to 19.47°. This theory, based on stationary phase arguments, is widely used both at
theoretical and technical levels. Yet a recent study by Rabaud and Moisy based on the observation of airborne images showed that the wake angle seems to decrease as the Froude number Fr increases, scaling as 1/Fr for large Froude numbers, thus challenging the commonly accepted theory of Lord Kelvin. But to explain such observations the authors make the strong hypothesis that an object of size b cannot generate wavelengths larger than b thus leading to unrealistic pressure fields to model the object. These results have raised the attention of the community and have been subjected to questioning. Darmon, Benzaquen and Raphael provide a solution to the propose an explanation of such observations without relaying on unphysical assumptions. They analytically show that the angle corresponding to the maximum amplitude of the waves scales as 1/Fr for large Froude numbers whereas the angle delimiting the wake region outside which the surface is essentially flat remains constant and equal to the Kelvin angle for all Fr. "And to think we could have doubted one of the greatest minds of the Victorian era!" concludes Hamish Johnson on Physics World.

A solution to the Kelvin wake angle controversy

Article by Hamish Johnson on Physics World


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