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Turbulent buoyant convection from a source in a confined two-layered region

Published online by Cambridge University Press:  20 April 2006

Mikio Kumagai
Mikio Kumagai
Affiliation:
Research School of Earth Sciences, The Australian National University, G.P.O. Box 4, Canberra, A.C.T. 2601, Australia Permanent address: Department of Chemical Engineering, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113, Japan.
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Abstract

We consider the time evolution of a layer of fresh water placed on top of a layer of salt water in a laboratory tank when denser salt water is supplied to a nozzle at the free surface. The inflow is carried out slowly so as to form a pure plume, which at first does not penetrate through the interface. The two basic processes that govern the time evolution of the initially fresh-water layer are the filling-box process (Baines & Turner 1969) and the entrainment through the end of the plume which impinges upon the density interface. A theoretical model that takes these two processes into account is presented, with the numerical solution of the asymptotic state, valid at large times. The asymptotic solution and experiment are in good agreement; the theory describes well the vertical buoyancy profile, the change in buoyancy difference across the interface with time, and the time when the plume begins to penetrate through the interface. The entrainment rate obtained from changes in thickness of the upper layer with time can be expressed as a function of the Froude number. The functional dependence is close to Fr3 at small values of Fr, and it approaches a finite limit as Fr increases. The buoyancy flux across the interface, which is non-dimensionalized by the rate of buoyancy input, also changes as a function of Fr, taking a maximum value of 0.168 at Fr = 0.46 and decreasing sharply at larger and smaller Froude numbers. These values agree well with those found from field observations and experiments on the entrainment at the boundary of convectively mixed layers. It is pointed out that some earlier results of Baines (1975) are not consistent with the model presented here.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 147 , October 1984 , pp. 105 - 131
Copyright
© 1984 Cambridge University Press

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