Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-08T05:35:19.829Z Has data issue: false hasContentIssue false
  • English
  • Français

Selective withdrawal and spin-up of a rotating stratified fluid

Published online by Cambridge University Press:  26 April 2006

S. G. Monismith  and
T. Maxworthy
S. G. Monismith
Affiliation:
Environmental Fluid Mechanics Laboratory, Department of Civil Engineering, Stanford University, Stanford, CA 94305-4020, USA
T. Maxworthy
Affiliation:
Departments of Mechanical and Aerospace Engineering, University of Southern California, University Park, Los Angeles, CA 90089-1453, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

We present an experimental study demonstrating that rotation has a pronounced effect on currents induced by selective withdrawal of fluid from a density-stratified reservoir. Our observations show that initiating outflow from the reservoir generates Kelvin shear waves. These waves propagate cyclonically around the perimeter of the reservoir, establishing an anticyclonic withdrawal-layer flow. This flow accelerates owing to the production of relative vorticity by compression of ‘planetary’ vorticity. The withdrawal-layer thickness as shown by vertical profiles of the horizontal velocity grows with time. Separation of the side-wall boundary layers in the corners of the tank causes the spun-up flow to eventually break up into a series of counterrotating gyres. We also present a model that describes many features of the spin-up process observed before onset of separation and subsequent gyre formation. The model shows that vertical diffusion of vorticity plays an important role in the spin up process, leading us to conclude that apparent thickening of the withdrawal layer over time, as seen in changes in the velocity profile, is associated with the vertical diffusion of the spun-up vorticity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 199 , February 1989 , pp. 377 - 401
Copyright
© 1989 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 An Introduction to Fluid Dynamics. Cambridge University Press.
Buzyna, G. & Veronis, G., 1971 Spin-up of a stratified fluid: theory and experiment. J. Fluid Mech. 50, 579–608.Google Scholar
Dahlquist, G. & Björk, A. 1974 Numerical Methods. Prentice Hall.
Gill, A. E.: 1976 Adjustment under gravity in a rotating channel. J. Fluid Mech. 77, 603–621.Google Scholar
Gill, A. E.: 1982 Atmosphere-Ocean Dynamics. Academic.
Greenspan, H. P.: 1968 The Theory of Rotating Fluids. Cambridge University Press.
Hide, R. & Mason, P. J., 1975 Sloping convection in a rotating fluid. Adv. Phys. 24, 47–100.Google Scholar
Imberger, J.: 1980 Selective withdrawal: a review. IAHR Proc. Second Intl Symp. on Stratified Flows, Trondheim, Norway, vol. 1, pp. 381–400.Google Scholar
Imberger, J. & Hamblin, P. F., 1982 Dynamics of lakes, reservoirs and cooling ponds. Ann. Rev. Fluid Mech. 14, 153–187.Google Scholar
Imberger, J., Thompson, R. O. R. Y. & Fandry, C. 1976 Selective withdrawal from a finite rectangular tank. J. Fluid Mech. 70, 489–512.Google Scholar
Ivey, G. N. & Blake, S., 1985 Axisymmetric withdrawal and inflow in a density-stratified container. J. Fluid Mech. 161, 115–137.Google Scholar
Kranenburg, C.: 1980 Selective withdrawal from a rotating two-layer fluid. IAHR Proc. Second Intl Symp. on Stratified Flows, Trondheim, Norway, vol. 1, pp. 401–410.Google Scholar
Lawrence, G. A.: 1980 Selective withdrawal through a point sink. Proc. Second Intl Symp. on Stratified Flows, Trondheim, Norway, vol. 1, pp. 411–423.Google Scholar
Maxworthy, T.: 1983 Experiments on solitary internal Kelvin waves. J. Fluid Mech. 129, 365–383.Google Scholar
Maxworthy, T. & Browand, F. K., 1975 Experiments in rotating and stratified flows: oceanographic application. Ann. Rev. Fluid Mech. 7, 273–305.Google Scholar
Narimousa, S. & Maxworthy, T., 1985 Two-layer model of shear-driven coastal upwelling in the presence of bottom topography. J. Fluid Mech. 159, 503–531.Google Scholar
Pao, H. P. & Kao, T. W., 1974 Dynamics of establishment of selective withdrawal of a stratified fluid from a line sink. Part 1. Theory. J. Fluid Mech. 65, 657–688.Google Scholar
Patterson, J. C., Hamblin, P. F. & Imberger, J., 1984 Classification and dynamics of the vertical density structure of lakes. Limnol. Oceanogr. 29, 845–861.Google Scholar
Silvester, R.: 1978 An experimental study of end-wall effects on selective withdrawal from a reservoir. PhD thesis, Department of Mechanical Engineering, University of Western Australia.
Spigel, R. H. & Farrant, B., 1984 Selective withdrawal through a point sink and pycnocline formation in a linearly stratified flow. J. Hydraul. Res. 22, 35–51.Google Scholar
Whitehead, J. A.: 1980 Selective withdrawal of a rotating stratified fluid. Dyn. Atmos. Oceans 5, 123–135.Google Scholar