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Selective withdrawal in rotating fluids

Published online by Cambridge University Press:  29 March 2006

Hsing-Hua Shih
Affiliation:
Department of Aerospace and Atmospheric Sciences, The Catholic University of America, Washington, D.C.
Hsien-Ping Pao
Affiliation:
Department of Aerospace and Atmospheric Sciences, The Catholic University of America, Washington, D.C.

Abstract

An axisymmetric flow of a rotating fluid into a point sink was studied experimentally. The type of motion is mainly controlled by the value of the Rossby number R, a ratio of inertial and Coriolis forces. Experimental investigation shows that at a sufficiently large value of R the fluid motion resembles potential flow. However, as R falls below a critical number the withdrawal of the fluid starts to be selective. The flow field then divides into two regions; namely, a central flowing core and an almost stagnant region surrounding it.

It is observed that at a Rossby number below the critical value the flow field, induced by a sudden start of discharge at the sink, experiences several distinct stages during the course of each run. At the initial moment the flow exhibits a feature of potential flow. During the second stage, it develops into a state of selective withdrawal with an inviscid profile of a flowing core, which is the main interest of the present study. In the third stage, due to the unavoidable influence of the free or solid surface at the upstream, flow undergoes another change. The flowing core becomes a fast-spinning jet, in which the viscous force becomes important.

It is also found that once selective withdrawal begins, the angular velocity and flow rate of the flowing core differ substantially from the basic rotation and the actual discharge at the sink. During this second stage of flow development, the flowing core tends to adjust itself such that the intrinsic Rossby number R′(= Wmax/2Ωcδc) based on the properties of the flowing core, virtually remains constant for all values of R below the critical value. This constant value of R′ is found to be about 0·36. The critical value of R which marks the beginning of the selective withdrawal is found to be in the neighbourhood of 0·26.

Type
Research Article
Copyright
© 1971 Cambridge University Press

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References

Baker, D. J. 1966 J. Fluid Mech. 26, 573.
Davis, W. & Fox, R. W. 1967 J. Basic Engrg. ASME Paper no. 66-WA/FE-21, 771.
Debler, W. R. 1959 Proc. Am. Soc. civil Engrs. 85, 51.
Greenspan, H. P. 1968 The Theory of notating Fluids. Cambridge University Press.
Hide, R. 1968 J. Fluid Mech. 32, 737.
Kao, T. W. 1965 J. Fluid Mech. 21, 535.
Kao, T. W. 1970 Phys. Fluids, 13, 558.
Lewellen, W. S. 1965 A.I.A.A.J. 3, 91.
Long, R. R. 1954 J. Met. 11, 247.
Long, R. R. 1956 Quart. J. Mech. Appl. Math. 9, 358.
Maxworthy, T. 1968 J. Fluid Mech. 31, 643.
Morgan, G. W. 1953 Proc. Cam. Phil. Soc. 49, 362.
Pao, H. P. & Kao, T. W. 1969 Phys. Fluids, 12, 1536.
Pritchard, W. G. 1969 J. Fluid Mech. 39, 443.
Schraub, F. A., Kline, S. J., Henry, J., Runstadler, J. W. & Littell, A. 1965 J. Basic Engrg ASME Paper no. 64-WA/FE-20.
Taylor, G. I. 1921 Proc. Roy. Soc. A 100, 114.
Trustrum, K. 1964 J. Fluid Mech. 19, 415.
Yih, C. S. 1958 Proc. 3rd U.S. Nat. Cong. Appl. Mech. 857.
Yih, C. S. 1965 Dynamics of Non-Homogeneous Fluids. New York: Macmillan.
Yih, C. S. 1969 Annual Review of Fluid Mech. 1, 98.