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Interaction between gravity waves and a shear flow

Published online by Cambridge University Press:  28 March 2006

B. A. Hughes  and
R. W. Stewart
B. A. Hughes
Affiliation:
Institute of Oceanography and Department of Physics, University of British Columbia, Vancouver 8, B.C.
R. W. Stewart
Affiliation:
Institute of Oceanography and Department of Physics, University of British Columbia, Vancouver 8, B.C.
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Abstract

A series of experiments has been undertaken in which three major properties of a surface tension-gravity wave system have been examined. The results of these experiments have been compared with existing theories. The three properties are: (i) viscous decay in the absence of mean flow, the relevant theory being given in Lamb (1932, § 348); (ii) propagation velocities in the presence and absence of flow (Lamb 1932, § 267), and (iii) the change of wave energy on crossing a stable Couette shear flow. The measurements in the last case were compared with two theories, one obtained from the Navier–Stokes equations including terms up to second order in wave slope, the other, following previous authors, obtained on the assumption that any direct interaction of the waves with the shear flow is negligible. According to the theory obtained from the Navier–Stokes equations, the divergence of surface wave energy is equal to the rate of change of wave energy due to the interaction between the mean flow and the wave system plus the rate of change of wave energy due to viscous decay.

An optical system was used to measure the maximum wave slopes, the wave-numbers and the shear velocities.

Results indicate that an anomalous region of wave properties exists for wave-numbers near 2.7 cm−1. For a set of data in which the wave-numbers were always less than 1.8 cm−1, it was found that the viscous decay rate and the propagation laws agree with theory to within the experimental error, and the interaction measurements fit the theory with the non-linear term included rather than the traditional theories.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 10 , Issue 3 , May 1961 , pp. 385 - 400
Copyright
© 1961 Cambridge University Press

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References

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