Buoyant Instability of a Viscous Film Over a Passive Fluid
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Authors
Canright, David R.
Morris, S.
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1993
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Abstract
In certain geophysical contexts such as lava lakes and mantle convection, a cold, viscous boundary layer forms over a deep pool. The following model problem investigates the buoyant instability of the layer. Beneath a shear-free horizontal boundary, a thin layer (thickness d1) of very viscous _uid overlies a deep layer of less dense, much less viscous _uid; inertia and surface tension are negligible. After the initial unstable equilibrium is perturbed, a long-wave analysis describes the growth of the disturbance, including the nonlinear e_ects of large amplitude. The results show that nonlinear e_ects greatly enhance growth, so that initial local maxima in the thickness of the viscous _lm grow to in_nite thickness in _nite time, with a timescale 8ﾵ/__ gd1. In the _nal catastrophic growth the peak thickness is inversely proportional to the remaining time. (A parallel analysis for _uids with power-law rheology shows similar catastrophic growth.) While the small-slope approximation must fail before this singular time, the failure is only local, and a similarity solution describes how the peaks become downwelling plumes as the viscous _lm drains away.
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The article of record as published may be located at http://dx.doi.org/10.1017/S0022112093002514
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Applied Mathematics
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Journal of Fluid Mechanics / Volume 255, 349-372
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.