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Selective withdrawal and blocking wave in rotating fluids

Published online by Cambridge University Press:  29 March 2006

Hsien-Ping Pao ,
Hsing-Hua Shih  and
Timothy W. Kao
Hsien-Ping Pao
Affiliation:
Department of Aerospace and Atmospheric Sciences, The Catholic University of America, Washington
Hsing-Hua Shih
Affiliation:
Department of Aerospace and Atmospheric Sciences, The Catholic University of America, Washington Present address: Biotechnology program, Carnegie-Mellon University, Pittsburg, Pa.
Timothy W. Kao
Affiliation:
Department of Aerospace and Atmospheric Sciences, The Catholic University of America, Washington
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Abstract

An analysis is made of the axially symmetric flow of a rotating inviscid incompressible fluid into a point sink a t sufficiently low values of the Rossby number. Based on the experimental observations, a theoretical flow model involving a surface of velocity discontinuity which separates the central flowing core from the surrounding stagnant region is proposed. A family of solutions is obtained after posing the problem as one involving a free streamline which is the line of velocity discontinuity in the axial plane. It is found that the flow possesses a minimum flow force as well as a minimum energy flux. Corresponding to such a state, a unique intrinsic Rossby number R′ based on the properties of the flowing core with a value of 1/[npar ]8 is determined. A discussion is made of the flow field development induced by a sudden start of a sink discharge. A theoretical model involving a blocking wave propagating upstream is proposed. The speeds of blocking waves are found to be higher than the maximum group velocity of the infinitesimal waves for R > 0.06. On the other hand, for R < 0.03, the waves are linear and dispersive in nature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 57 , Issue 3 , 20 February 1973 , pp. 459 - 480
Copyright
© 1973 Cambridge University Press

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