Journal of Fluid Mechanics

The unstable thermal interface

J. W.  Elder a1
a1 Department of Applied Mathematics and Theoretical Physics, Cambridge

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The motion which develops in a deep layer of a viscous, thermally conducting fluid initially hot below and cold above some horizontal plane, so that the system is gravitationally unstable, is studied by laboratory and numerical experiments. Three cases are considered: (i) the flow which occurs in a porous medium when the interface is the lower boundary of the system; (ii) a similar study in a viscous fluid; (iii) an interface distant from the confining horizontal boundaries, in a viscous fluid. In all cases the initial development of the flow—assuming an initial source of noise, for example as temperature fluctuations—occurs within the thermal interface between the hot and cold fluid. The scale of the motion is set by the thickness of the interface.

The development of the disturbances in the interface involves: a period of local thickening and induced, damped motions in which the diffusion of heat and vorticity dominate; a period of gestation, involving rapid amplification, with the disturbance imbedded in the interface and diminishing importance of the role of diffusion of heat; a period of emergence of the disturbances from the interface, during which the accelerations are sufficiently rapid for molecular processes to be unimportant, entrainment being the dominant process, and the gravitational energy accumulated locally in the interface is largely removed; and finally a period of adjustment of the large eddies. The amplification process is adequately described by the linearized equations of motion.

(Published Online March 28 2006)
(Received February 27 1967)
(Revised October 17 1967)