Non-modal behavior in the linear regime of high-speed boundary layer flows: Flow–thermodynamic interactions

Abstract

The flow–thermodynamic interactions in the transient linear regime of high-speed boundary layers starting from non-modal initial conditions are studied using direct numerical simulation. These simulations are performed at different Mach numbers: M∈[3,6]. The perturbation velocity field is decomposed into solenoidal and dilatational components using the Helmholtz decomposition. It is shown that at high speeds, random pressure perturbations evolve to their asymptotic state in three distinct stages. In stage 1, pressure–dilatation engenders rapid transfer from internal to kinetic energy leading to a balance between the two forms. Pressure–dilatation maintains this balance throughout stage 2 with harmonic exchange of energy between the two forms. During this stage, the stable modes decay and the unstable modes establish ascendancy. Stage 3 behavior is dominated almost exclusively by the most unstable mode. Both internal and kinetic energies grow at the rate predicted by linear stability analysis. At this stage, pressure–dilatation is small and production dominates the flow evolution. This behavior is also observed in narrow-band perturbation evolution. Spatial boundary layer simulations are also performed to examine the non-parallel effects on the observed behavior. It is seen that the role of pressure–dilatation essentially remains the same as observed in the parallel flow case.