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Selective withdrawal from a finite rectangular tank

Published online by Cambridge University Press:  11 April 2006

Jorg Imberger ,
Rory Thompson  and
Chris Fandry
Jorg Imberger
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6009
Rory Thompson
Affiliation:
Department of Mathematics, The University of Western Australia, Nedlands, Western Australia 6009 Geofysisk Institutt, Universitetet i Bergen, Bergen, N 5000, Norway.
Chris Fandry
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria 3168, Australia
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Abstract

The time development of two-dimensional fluid motion induced by a line sink in a rectangular, density stratified reservoir with a free surface is given. It is shown that the initiation of such a sink gives birth to a spectrum of internal expanding shear fronts with a progressively decreasing vertical wavelength. These fronts move out from the sink and travel towards the far wall, where they are reflected. This process ceases once the front with a vertical wavelength equal to the steady withdrawal-layer thickness has reached the end wall. The fronts so introduced continue to move back and forth, expanding to standing waves if the viscosity of the fluid is small enough. The evolution and nature of the withdrawal layer are shown to depend critically on the relative magnitude of the convective inertia and viscous forces, the number of reflexions from the rear wall and the Prandtl number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 3 , 7 December 1976 , pp. 489 - 512
Copyright
© 1976 Cambridge University Press

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References

Birdsall Charles, K. & Fuss, D. 1969 J. Comp. Phys. 3, 494–510.
Darden, B. R., Imberger, J. & Fischer, H. B. 1972 A.S.C.E.J. Hydraul. Div. 101, 1211–1220.
Gelhar, L. W. & Mascolo, D. M. 1966 M.I.T. Hydraul. Lab. Rep. no. IV 088, pp. 1–39.
Harlow, F. H. & Welsh, J. E. 1965 Phys. Fluids, 8, 2182–2183.
Kao, W. T. 1970 Phys. Fluids, 13, 535–543.
Kao, W. T., Pao, H. P. & Wei, S. N. 1974 J. Fluid Mech. 65, 689–710.
Janowitz, G. S. 1968 J. Fluid Mech. 33, 417–432.
Imberger, J. 1972 J. Fluid Mech. 53, 329–349.
Imberger, J. & Fandry, C. B. 1975 J. Fluid Mech. 70, 321–332.
Mcewan, A. D. & Baines, P. G. 1974 J. Fluid Mech. 63, 257–272.
Manins, P. C. 1976 J. Fluid Mech. 74, 547–560.
Maxworthy, T. 1972 IAHR/AIRH Int. Symp. Stratified Flows, Novosibirsk, paper 17.
Pao, H. P. & Kao, W. T. 1974 J. Fluid Mech. 65, 657–688.
Silvester, R. 1977 Ph.D. thesis, University of Western Australia.
Thompson, R. O. R. Y. 1976 J. Fluids & Comp. (in Press).
Wood, I. R. & Lai, K. K. 1972 J. Hydraul Res. 10, 475–496.
Zuluaga-Angel, A., Darden, R. B. & Fischer, H. B. 1972 U.S. Environ. Protection Agency Rep. no. R2-72-037. Washington D.C.