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The free compressible viscous vortex

Colonius, Tim and Lele, Sanjiva K. and Moin, Parviz (1991) The free compressible viscous vortex. Journal of Fluid Mechanics, 230 . pp. 45-73. ISSN 0022-1120. https://resolver.caltech.edu/CaltechAUTHORS:20190726-104729209

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Abstract

The effects of compressibility on free (unsteady) viscous heat-conducting vortices are investigated. Analytical solutions are found in the limit of large, but finite, Reynolds number, and small, but finite, Mach number. The analysis shows that the spreading of the vortex causes a radial flow. This flow is given by the solution of an ordinary differential equation (valid for any Mach number), which gives the dependence of the radial velocity on the tangential velocity, density, and temperature profiles of the vortex; estimates of the radial velocity found by solving this equation are found to be in good agreement with numerical solutions of the full equations. The experiments of Mandella (1987) also report a radial flow in the vortex, but their estimates are much larger than the analytical predictions, and it is found that the flow inferred from the experiments violates the Second Law of Thermodynamics for two-dimensional axisymmetric flow. It is speculated that three-dimensionality is the cause of this discrepancy. To obtain detailed analytical solutions, the equations for the viscous evolution are expanded in powers of Mach number, M. Solutions valid to O(M^2), are discussed for vortices with finite circulation. Two specific initial conditions - vortices with initially uniform entropy and with initially uniform density - are analysed in detail. It is shown that swirling axisymmetric compressible flows generate negative radial velocities far from the vortex core owing to viscous effects, regardless of the initial distributions of vorticity, density and entropy.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1017/S0022112091000708DOIArticle
ORCID:
AuthorORCID
Colonius, Tim0000-0003-0326-3909
Additional Information:© 1991 Cambridge University Press. Received 22 June 1990; in revised form 21 December 1990; published online 26 April 2006. This work was supported by the Office of Naval Research under contract number ONR-N00014-88-K-0592. The computer time was provided by NASA Ames Research Center.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-88-K-0592
Record Number:CaltechAUTHORS:20190726-104729209
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190726-104729209
Official Citation:Colonius, Tim, Sanjiva K. Lele, and Parviz Moin. "The Free Compressible Viscous Vortex." Journal of Fluid Mechanics 230 (1991): 45–73. doi:10.1017/S0022112091000708.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97449
Collection:CaltechAUTHORS
Deposited By: Melissa Ray
Deposited On:31 Jul 2019 15:43
Last Modified:03 Oct 2019 21:31

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