A Study of the Unstable Modes in High Mach Number Gaseous Jets and Shear Layers

by Gene Marcel Bassett

Under the supervision of Professor Paul W. Woodward

ABSTRACT

Instabilities affecting the propagation of supersonic gaseous jets have been studied using high resolution computer simulations with the Piecewise-Parabolic-Method (PPM). These results are discussed in relation to jets from galactic nuclei. These studies involve a detailed treatment of a single section of a very long jet, approximating the dynamics by using periodic boundary conditions. Shear layer simulations have explored the effects of shear layers on the growth of nonlinear instabilities. Convergence of the numerical approximations has been tested by comparing jet simulations with different grid resolutions. The effects of initial conditions and geometry on the dominant disruptive instabilities have also been explored.
 
Simulations of shear layers with a variety of thickness, Mach numbers and densities perturbed by incident sound waves imply that the time for the excited kink modes to grow large in amplitude and disrupt the shear layer is tg = (546 ± 24) (M/4)^1.7 (Apert/0.02)^-0.4 d/c , where M is the jet Mach number, d is the half-width of the shear layer, and Apert is the perturbation amplitude.
 
For simulations of periodic jets, the initial velocity perturbations set up zig-zag shock patterns inside the jet. In each case a single zig-zag shock pattern (an odd or bending mode) or a double zig-zag shock pattern (an even or pinching mode) grows to dominate the flow. The dominant kink instability responsible for these shock patterns moves approximately at the linear resonance velocity, vmode = cext*vrelative/( cjet + cext). For high resolution simulations (those with 150 or more computational zones across the jet width), the even mode dominates if the even perturbation is higher in amplitude initially that the odd perturbation. For low resolution simulations, the odd mode dominates even for a stronger even mode perturbation. In high resolution simulations the jet boundary rolls up and large amounts of external gas are entrained into the jet. In low resolution simulations this entrainment process is impeded by numerical viscosity. The three-dimensional jet simulations behave similarly to two-dimensional jet runs with the same grid resolutions.