Hostname: page-component-848d4c4894-4rdrl Total loading time: 0 Render date: 2024-06-19T23:03:50.237Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1967 Am Introduction to Fluid Dynamics. Cambridge University Press.
Benjamin, T. B. 1970 J. Fluid Mech. 40, 49.
Bretherton, F. P. & Turner, J. S. 1968 J. Fluid Mech. 32, 449.
Debler, W. R. 1959 Proc. A.S.C.E. 85, 51.
Fraenkel, L. E. 1956 Proc. Roy. SOC. A 33, 506.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Kao, T. W. 1965a J. Fluid Mech. 21, 535.
Kao, T. W. 1965b J. Geophys. Res. 70, 815.
Kao, T. W. 1970 Phys. Fluids, 13, 558.
Lamb, H. 1932 Hydrodynamics. Dover.
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Long, R. R. 1954 Tellus, 6, 97.
Long, R. R. 1956 Quart. J. Mech. Appl. Math. 9, 358.
Long, R. R. 1970 Tellus, 22, 471.
Pao, H.-P. & Kao, T. W. 1972 Unsteady rotating flow into apoint sink. Dept. Aerospace & Atmospheric Sciences, The Catholic University of America Rep. HY-72-004.Google Scholar
Rayleigh, Lord 1880 ScientiJic Papers, vol. 1, 474. Cambridge University Press.
Scorer, R. S. 1965 Sci. J. 2, 46.
Shih, H.-H. & Pao, H.-P. 1971 J. Fluid Mech. 49, 509.
Trustrum, K. 1964 J. Fluid Mech. 19, 415.
Veronis, G. 1970 Annual Rev. Fluid Mech. 2, 37.