The nonlinear instability of the supersonic crossflow vortex

Abstract

The crossflow instability is an important factor of triggering the turbulent transition in swept wing flows, at present, major works focus on incompressible three-dimensional boundary layer flows. In this paper, the crossflow nonlinear instability in a swept wing flow is investigated using the nonlinear parabolized stability equation (NPSE) for free stream Mach number Ma=0.05, Ma=0.7 and Ma=1.5 cases. We find that the crossflow vortex turns out to be more unstable and the magnitude of minimum local streamwise vorticity increases when the free stream Mach number increases. The influence of free stream Mach number on crossflow secondary instability is investigated using the Flouqet theory, it can be seen that secondary instability ‘z’ modes are amplified with increasing the free stream Mach number, however, the maximum growth rate of the secondary instability ‘y’ mode is almost in-dependent on free stream Mach number. Although experimental results of turbulent transition in incompressible three dimensional boundary layers confirmed that the crossflow transition was insensitive to free stream acoustic fluctuations, we observe acoustic modes in the spectrum of supersonic swept wing flow, emphasizing qualitative features of fast travelling acoustic modes.