Parametric Instabilities in Time-Varying Compressible Linear Flows - Ioannis Kiorpelidis; Nikolaos A. Bakas (Fluids)
The stability of time-dependent compressible linear flows, which are characterized by periodic variations in either their shape or their shear, is investigated. Two novel parametric instabilities are found: an instability that occurs for periodically wobbling elliptic vortices at a number of discrete oscillation frequencies that are proportional to the Mach number and an instability that occurs for all linear flows at various frequencies of the shear oscillation that depend on the Mach number. In addition, the physical mechanism underlying the instabilities is explained in terms of the linear interaction of three waves with time-varying wavevectors that describe the evolution of perturbations: a vorticity wave representing the evolution of incompressible perturbations and two counter-propagating acoustic waves. Elliptical instability occurs because the scale of the acoustic waves decreases exponentially and their wave action is conserved, leading to an exponential increase in the acoustic waves’ energies. The instability in shear-varying flows is driven by the interaction between vorticity and the acoustic waves, which couple through the shear and for specific frequencies resonate parametrically, leading to exponential or linear growth.