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Local stability analysis of an inviscid transverse jet

Published online by Cambridge University Press:  22 May 2007

LEONARDO S. de B. ALVES ,
ROBERT E. KELLY  and
ANN R. KARAGOZIAN
LEONARDO S. de B. ALVES
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095-1597, USA
ROBERT E. KELLY
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095-1597, USA
ANN R. KARAGOZIAN
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, Los Angeles, CA 90095-1597, USA
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Abstract

A local linear stability analysis is performed for a round inviscid jet with constant density that is injected into a uniform crossflow of the same density. The baseflow is obtained from a modified version of the inviscid transverse jet near-field solution of Coelho & Hunt (J. Fluid Mech. vol. 200, 1989, p. 95) which is valid for small values of the crossflow-to-jet velocity ratio λ. A Fourier expansion in the azimuthal direction is used to couple the disturbances with the three-dimensional crossflow. The spatial growth rates of the modes corresponding to the axisymmetric and first helical modes of the free jet as λ → 0 increase as λ increases. The diagonal dominance of the dispersion relation matrix is used as a quantitative criterion to estimate the range of velocity ratios (0 < λ < λc) within which the transverse jet instability can be considered to have a structure similar to that of the free jet. Further, we show that for λ>0 positive and negative helical modes have different growth rates, suggesting an inherent weak asymmetry in the transverse jet.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 581 , 25 June 2007 , pp. 401 - 418
Copyright
Copyright © Cambridge University Press 2007

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