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Finite-Amplitude Instability of the Compressible Laminar Wake. Strongly Amplified Disturbances

Liu, J. T. C. and Lees, Lester (1970) Finite-Amplitude Instability of the Compressible Laminar Wake. Strongly Amplified Disturbances. Physics of Fluids, 13 (12). pp. 2932-2938. ISSN 1070-6631.

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The interaction between mean flow and finite‐amplitude disturbances in certain experimentally observed unstable, compressible laminar wakes is considered theoretically without explicitly assuming small amplification rates. Boundary‐layer form of the two‐dimensional mean‐flow momentum, kinetic energy and thermal energy equations and the time‐averaged kinetic energy equation of spatially growing disturbances are recast into their respective von Kármán integral form which show the over‐all physical coupling. The Reynolds shear stresses couple the mean flow and disturbance kinetic energies through the conversion mechanism familiar in low‐speed flows. Both the mean flow and disturbance kinetic energies are coupled to the mean‐flow thermal energy through their respective viscous dissipation. The work done by the disturbance pressure gradients gives rise to an additional coupling between the disturbance kinetic energy and the mean‐flow thermal energy. The compressibility transformation suggested by work on turbulent shear flows is not applicable to this problem because of the accompanying ad hoc assumptions about the disturbance behavior. The disturbances of a discrete frequency which corresponds to the most unstable fundamental component, are first evaluated locally. Subsequent mean‐flow and disturbance profile‐shape assumptions are made in terms of a mean‐flow‐density Howarth variable. The compressibility transformation, which cannot convert this problem into a form identical to the low‐speed problem of Ko, Kubota, and Lees because of the compressible disturbance quantities, nevertheless, yields a much simplified description of the mean flow.

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Additional Information:© 1970 American Institute of Physics. Received 2 January 1970; final manuscript received 22 July 1970. The research reported in this paper is supported in part by the National Science Foundation through Grant GK-10008 at Brown University (J.T.C.L.) and in part by the United States Army Research Office and the Advanced Research Projects Agency through Contract No. DA-31-124-ARO(D)-33 at the California Institute of Technology (L.L.).
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Army Research Office (ARO)UNSPECIFIED
Advanced Research Projects Agency (ARPA)DA-31-124-ARO(D)-33
Issue or Number:12
Record Number:CaltechAUTHORS:20120810-112829770
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Official Citation:Finite-Amplitude Instability of the Compressible Laminar Wake. Strongly Amplified Disturbances J. T. C. Liu and Lester Lees, Phys. Fluids 13, 2932 (1970), DOI:10.1063/1.1692884
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33089
Deposited By: Aucoeur Ngo
Deposited On:10 Aug 2012 20:20
Last Modified:03 Oct 2019 04:06

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