Stability of compressible streamwise vortices

Abstract

A sufficient condition for instability of full compressible inviscid streamwise vortices has been derived using asymptotic analysis with large wavenumbers. Based on the nature of instability, the obtained growth rate is described using an entropy instability term, a spiral instability term, a helicity instability term, and an acoustic instability term. The entropy instability term correlates with compressibility. The spiral instability term is reasonably expressed by the axial and azimuthal velocities and their wavenumbers. The helicity instability term depends on the helicity profiles. In particular, the unstable condition for wake-type flows is satisfied when they possess a negative helicity in the profiles. The acoustic instability term depends on the local speed of sound. Linear and nonlinear numerical simulations are used to validate the instability conditions. The effect of the helicity instability is shown to be significantly strong by the simulations.