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Stability of an oscillated fluid with a uniform density gradientInstabilities in a fluid with a constant density gradient that is subject to arbitrarily oriented oscillatory accelerations are considered. With the Boussinesq approximation and for the case of an unbounded fluid, transformation to Lagrangian coordinates allows the reduction of the problem to an ordinary differential equation for each three-dimensional wavenumber. The problem has three parameters: the nondimensional amplitude R of the base-state oscillation, the nondimensional level of background steady acceleration, which for some cases can be represented in terms of a local (in time) Richardson number Ri, and the Prandtl number Pr. Some general bounds on stability are derived. For Pr = 1 closed-form solutions are found for impulse (delta function) accelerations and a general asymptotic solution is constructed for large R and general imposed accelerations. The asymptotic solution takes advantage of the fact that at large R wave growth is concentrated at 'zero points'. These are times when the effective vertical wavenumber passes through zero. Kelvin-Helmholtz instabilities are found to dominate at low R, while Rayleigh-Taylor instabilities dominate at high R. At high R, the uniform shear of the Kelvin-Helmholtz case tends to distort and weaken instability waves. With unsteady flows, Ri = 1/4 is no longer an instability limit. Significant instabilities have been found for sinusoidal forcing for Ri up to 0.6.
Document ID
19910028348
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Jacqmin, David
(NASA Lewis Research Center Cleveland, OH, United States)
Date Acquired
August 14, 2013
Publication Date
October 1, 1990
Publication Information
Publication: Journal of Fluid Mechanics
Volume: 219
ISSN: 0022-1120
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
91A12971
Distribution Limits
Public
Copyright
Other

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