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Cross-waves. Part 2. Experiments

Published online by Cambridge University Press:  29 March 2006

B. J. S. Barnard  and
W. G. Pritchard
B. J. S. Barnard
Affiliation:
Fluid Mechanics Research Institute, University of Essex, Colchester
W. G. Pritchard
Affiliation:
Fluid Mechanics Research Institute, University of Essex, Colchester
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Abstract

In this paper experiments in which cross-waves were generated in front of a wave-maker at one end of a long channel are described. The primary field produced was a progressive wave train, but, at certain frequencies, a standing wave developed in front of the wavemaker. This wave, whose crests were at right angles to the wavemaker and which had frequency half that of the wavemaker, is known as a cross-wave.

An instability mechanism for the formation of cross-waves in a long channel has been presented in Part 1 (Mahony 1972). In the present paper we describe some measurements concerning the formation of the waves. The initial growth rate of the waves has been measured and the curves of neutral stability determined for two of the possible modes. The results are in good agreement with Mahony's theory. After the early stages in the development of the waves, there is an increase in their growth rate. This new rate was found to be about twice the initial growth rate. Also reported are some measurements of the amplitude of the cross-wave field along the channel.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 2 , 26 September 1972 , pp. 245 - 255
Copyright
© 1972 Cambridge University Press

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References

Garrett, C. J. R. 1970 On cross-waves. J. Fluid Mech. 41, 837.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics. Pergamon.
Mahony, J. J. 1972 Cross-waves. Part 1. Theory. J. Fluid Mech. 55, 229.Google Scholar
McGoldrick, L. F. 1968 Faraday waves: the cross-wave resonant instability. University of Chicago, Department of Geophysical Sciences. Tech. Rep. no. 2.Google Scholar