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Effect of compressibility on inhomogeneous planar shear flows: Stabilizing mechanisms

DOI: 10.1615/THMT-18.300
pages 325-334

Rebecca L. Bertsch
Department of Aerospace Engineering, Texas A&M University College Station, Texas 77843-3141, USA; Los Alamos National Laboratory, Los Alamos, USA

Divya Sri Praturi
Department of Aerospace Engineering, Texas A&M University, College Station, Texas, USA

Sharath S. Girimaji
Department of Aerospace Engineering, Texas A&M University, College Station, Texas, USA; Department of Ocean Engineering, Texas A&M University, College Station, Texas, USA


We investigate the effect of compressibility on inhomogeneous planar shear flows and contrast it against homogeneous shear flows. For this purpose Kolmogorov flow, a prototypical planar inhomogeneous periodic shear flow is studied. Homogeneous shear flows are subjected to algebraic growth of perturbations, where as, in a Kolmogorov flow, due to the presence of inflection points, the flow experiences modal instabilities at certain locations. Compressibility is shown to have clear stabilizing influences on both homogeneous and inhomogeneous shear flows. However, there are important differences in the nature of stabilization seen in both the flows. Homogeneous shear flows experience a three-stage stabilization of kinetic energy. On the other hand, kinetic energy in a compressible Kolmogorov flow is stabilized compared to its incompressible counterpart from the beginning. The reason for the immediate stabilization is due to the generation of higher normal wavenumbers in the flow even in the linear regime, due to the interactions between mean and perturbation components of the velocity field. The study provides insight into understanding and modeling compressible shear flows.

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