On the growth and propagation of linear instability waves in compressible turbulent jets

Abstract

The linear instability of compressible axisymmetric unheated jets is investigated numerically. Solutions to the linear parabolized stability equations with Reynolds-averaged Navier–Stokes mean flows are used to describe the streamwise evolution of instability waves. For transonic jets, helical (azimuthal mode number m=1) instability waves tend to exhibit the largest gain over the jet potential core followed by the m=2 and axisymmetric modes. At higher frequencies, the disparity in energy growth between the different azimuthal modes decreases, and there is a progressive reduction in energy growth as azimuthal mode number is increased from two to four. The entropic and pressure components of the total energy are compared to the kinetic energy. We find that the pressure term tends to be small, while the importance of the entropic component increases with frequency and decreases with azimuthal mode number. It is shown that the helical mode growth rates exhibit similarity when a local “mixing layer” scaling is adopted. This similarity is then used to concisely illustrate the stabilizing effect of compressibility over a broad range of frequencies and Mach numbers. Computed phase velocities are compared to measured convective velocities for unforced turbulent jets with Mach numbers Mj=0.51 and Mj=1.41. Good agreement is observed provided that the appropriate azimuthal mode number is selected.