Analytical prediction of low-frequency fluctuations inside a one-dimensional shock

Linear instability of high-speed boundary layers is routinely examined assuming quiescent edge conditions, without reference to the internal structure shocks or instabilities potentially generated in them. Our recent work has shown that kinetically modeled nonequilibrium zone straight away from solid boundaries exhibits low-frequency molecular fluctuations. The presence dominant low frequencies observed using direct simulation Monte Carlo (DSMC) method been explained as a consequence well-known bimodal probability density function (PDF) energy particles inside shock. Here, PDFs particle energies are derived upstream and downstream equilibrium regions, well shocks, it for first time they have form noncentral Chi-squared (NCCS) distributions. A linear correlation proposed relate change shape analytical at specified number temperature Mach number, within range $$3 \le M 10$$ , with DSMC-derived average characteristic computed our earlier work. At given $$M=7.2$$ $$n_1=10^{22}\,\hbox {m}^{-3}$$ variation correlated most-probable-speed location maximum bulk velocity gradient translational $$\sim 90 T_{tr,1}/(K) 1420$$ . Using functions, estimated ranges input semi-empirical relationship predict oscillations shocks. model can be used provide realistic physics-based conditions receptivity stability analysis studies laminar-turbulent transition flows.