Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-19T01:06:31.387Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent buoyant convection from a source in a confined region

Published online by Cambridge University Press:  19 April 2006

P. C. Manins
P. C. Manins
Affiliation:
CSIRO Division of Atmospheric Physics, Station Street, Aspendale, Victoria, Australia
Get access Rights & Permissions [Opens in a new window]

Abstract

An extension of the model first proposed by Baines & Turner (1969) is derived with careful attention to the conditions required for its application. The most important of these are that the Prandtl number ν/k is of order unity or greater, the ratio of the length L to depth H of the region is greater than about 1·2 for the two-dimensional region considered and R is so large that R [gsim ] L/H and R [Gt ] 1/α. The characteristic group \[ R\equiv \alpha^{\frac{2}{3}}F_0^{\frac{1}{3}}H/\nu. \]R2 is a Grashof number based on the source strength F0 of the buoyant convection which is modelled using turbulent plume theory and the entrainment constant α, the ratio of inflow velocity across the edge of the plume to mean local plume velocity. The conditions on R ensure that the source of buoyant convection is the dominant transportive mechanism in the region and the restrictions on the aspect ratio ensure that there is clear separation between the passive motions in the bulk of the region and the intense highly confined buoyant convection.

The manner in which the convective fluid recirculates to become part of the passive interior is studied and shown to be controlled by the same dynamics as fluid intrusion into a stably stratified environment.

Several new solutions are obtained, including cases of steady conditions involving only one source.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 4 , 27 April 1979 , pp. 765 - 781
Copyright
© 1979 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

Baines, W. D. 1975 Entrainment from a density interface by a plume or jet. J. Fluid Mech. 68, 309–320.Google Scholar
Baines, W. D. & Turner, J. S. 1969 Turbulent buoyant convection from a source in a confined region. J. Fluid Mech. 37, 51–80.Google Scholar
Batchelor, G. K. 1954 Heat convection and buoyancy effects in fluids. Quart. J. Roy. Met. Soc. 80, 339–358.Google Scholar
Cormack, D. E., Leal, L. G. & Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory. J. Fluid Mech. 65, 209–229.Google Scholar
Deardorff, J. W. 1966 The counter-gradient heat flux in the lower atmosphere and in the laboratory. J. Atmos. Sci. 23, 503–506.Google Scholar
Germeles, A. E. 1975 Forced plumes and mixing of liquids in tanks. J. Fluid Mech. 71, 601–623.Google Scholar
Gill, A. E. 1966 The boundary-layer regime for convection in a rectangular cavity. J. Fluid Mech. 26, 515–536.Google Scholar
Gray, D. D. & Giorgini, A. 1976 The validity of the Boussinesq approximation for liquids and gases. Int. J. Heat Mass Transfer 19, 545–551.Google Scholar
Imberger, J. 1974 Natural convection in a shallow cavity with differentially heated end walls. J. Fluid Mech. 65, 247–260.Google Scholar
Imberger, J., Thompson, R. O. R. Y. & Fandry, C. 1970 Selective withdrawal from a finite rectangular tank. J. Fluid Mech. 78, 489–512.Google Scholar
Killworth, P. D. & Manins, P. C. 1979 A model of confined thermal convection driven by nonuniform heating from below. To be submitted for publication.
Kotsovinos, N. E. & List, E. J. 1977 Plane turbulent buoyant jets. Part 1. Integral properties. J. Fluid Mech. 81, 25–44.Google Scholar
Manins, P. C. 1973a A filling box model of the deep circulation of the Red Sea. Mem. Soc. Roy. Sci. Liège, 6, 153–166.Google Scholar
Manins, P. C. 1973b Confined Convective Flows. Ph.D. thesis. University of Cambridge.
Manins, P. C. 1976 Intrusion into a stratified fluid. J. Fluid Mech. 74, 547–560.Google Scholar
Moore, D. R. & Weiss, N. O. 1973 Two-dimensional Rayleigh—Bénard convection. J. Fluid Mech. 58, 289–312.Google Scholar
Morton, B. R., Taylor, G. I. & Turner, J. S. 1956 Turbulent gravitational convection from maintained and instantaneous sources. Proc. Roy. Soc. A 234, 1–23.Google Scholar
Phillips, O. M. 1972 The entrainment interface. J. Fluid Mech. 51, 97–118.Google Scholar
Priestley, C. H. B. 1959 Turbulent Transfer in the Lower Atmosphere. University of Chicago Press.
Rouse, H., Yih, C. S. & Humphreys, H. W. 1952 Gravitational convection from a boundary source. Tellus 4, 201–210.Google Scholar
Stommel, H. 1962 On the smallness of sinking regions in the oceans. Proc. Natn. Acad. Sci., U.S.A. 38, 766–772.Google Scholar
Townsend, A. A. 1970 Entrainment and the structure of turbulent flow. J. Fluid Mech. 41, 13–46.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Van Dyke, M. 1975 Perturbation Methods in Fluid Mechanics. Stanford: The Parabolic Press.
Walin, G. 1971 Contained non-homogeneous flow under gravity or how to stratify a fluid in the laboratory. J. Fluid Mech. 48, 647–672.Google Scholar
Wesseling, P. 1969 Laminar convection cells at high Rayleigh number. J. Fluid Mech. 36, 625–637.Google Scholar
Wilkinson, D. L. & Wood, I. R. 1971 A rapidly varied flow phenomenon in a two-layer flow. J. Fluid Mech. 47, 241–256.Google Scholar
Wyrtki, K. 1961 The thermohaline circulation in relation to the general circulation in the oceans. Deep Sea Res. 8, 39–64.Google Scholar