Standing waves on a contracting or expanding current

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Abstract
In a recent work Longuet-Higgins & Stewart (1961) have studied the changes in wavelength and amplitude of progressive waves of constant frequency as they are propagated into regions of surface divergence or convergence. In the work here described the complementary conditions are assumed. Standing waves of uniform wavelength, λ, exist in an area of uniform surface divergence. Changes in amplitude and wavelength are studied. These changes depend on the existence of the radiation stress which was discovered by Longuet-Higgins & Stewart but the physical interpretation of this stress is simpler for standing than for progressive waves. Three different ways of obtaining the same rate of strain in the direction of the current caused the amplitude to vary as , respectively.Experiments in which free-standing waves were generated in a tank one wave-length wide which was then made narrower verified the conclusion that contraction does not alter the periodic character of the waves, even though the ratio of amplitude to wavelength becomes so great that they can no longer be treated mathematically by the usual linearized approximation. The shape of the profile then appears to agree well with calculations of Penney & Price (1952).

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