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Stabilizing action of pressure in homogeneous compressible shear flows: effect of Mach number and perturbation obliqueness

Published online by Cambridge University Press:  12 November 2014

G. Kumar ,
Rebecca L. Bertsch  and
Sharath S. Girimaji
G. Kumar
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
Rebecca L. Bertsch*
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
Sharath S. Girimaji
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
*
†Email address for correspondence: [email protected]
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Abstract

Compressibility exerts a stabilizing influence on a variety of high-speed shear flows such as turbulent mixing layers, transitioning boundary layers and homogeneously sheared turbulence. An important stabilizing feature that is common amongst all shear flows is the velocity–pressure interaction dynamics. In this study, velocity–pressure interactions of individual perturbation or fluctuation modes are investigated using direct numerical simulations and linear analysis in high-Mach-number homogeneous shear flow. For a given perturbation wave mode, the action of pressure is shown to depend on two important factors: the orientation of the perturbation wavevector with respect to the shear plane and the Mach number. It is shown that the streamwise perturbation wave mode rapidly develops a high level of kinetic energy but is self-limiting owing to the action of pressure. On the other hand, the energy of spanwise perturbation wave modes grows unaffected by pressure or Mach number. Oblique modes combine spanwise and streamwise characteristics and are shown to be chiefly responsible for stabilizing effects seen in shear flows. Three regimes of obliqueness of different linear stability characteristics are identified. The critical role of perturbation obliqueness on stabilization is established.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Homogeneous turbulence Turbulent Flows: Shear layer turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 760 , 10 December 2014 , pp. 540 - 566
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Copyright
© 2014 Cambridge University Press 

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