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A note on the application of a radiation condition for a source in a rotating stratified fluid

Published online by Cambridge University Press:  29 March 2006

A. Ramachandra Rao
Affiliation:
Department of Applied Mathematics, Indian Institute of Science, Bangalore 560012, India

Abstract

The motion due to an oscillatory point source in a rotating stratified fluid has been studied by Sarma & Naidu (1972) by using threefold Fourier transforms. The solution obtained by them in the hyperbolic case is wrong since they did not make use of any radiation condition, which is always necessary to get the correct solution. Whenever the motion is created by a source, the condition of radiation is that the sources must remain sources, not sinks of energy and no energy may be radiated from infinity into the prescribed singularities of the field. The purpose of the present note is to explain how Lighthill's (1960) radiation condition can be applied in the hyperbolic case to pick the correct solution. Further, the solution thus obtained is reiterated by an alternative procedure using Sommerfeld's (1964) radiation condition.

Type
Research Article
Copyright
© 1973 Cambridge University Press

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References

Erdélyi, A., Magnus, W. Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms, vols. 1 and 2. McGraw-Hill.
Lighthill, Xi. J. 1960 Phil. Trans. Roy. Soc. A 252, 397.
Sarma, L. V. K. V. & Naidu, K. B. 1972 Acta Mechanica, 13, 21.
Sommbrfeld, A. 1964 Partial Differential Equations in Physics. Academic.
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