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arXiv · 2512.11390

A Kinetic Study of Hypersonic Boundary Layer Second Mack Mode Instabilities

Mert Senkardesler·Irmak T. Karpuzcu·Deborah A. Levin
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Abstract

A flat-plate laminar boundary layer is simulated at a free stream Mach number of 6 and unit Reynolds number $Re_1 \sim 1.18\times 10^7$ m$^{-1}$ using the Direct Simulation Monte Carlo (DSMC) method to capture and analyze spontaneous second-mode instability growth. Power spectral density (PSD) analysis identifies dominant frequencies of 200-500 kHz, in line with linear stability theory (LST) predictions. Near-wall perturbations remain confined within the unstable regions known from linear theory. An analytic kinetic fluctuation floor was derived to predict the limit of the DSMC predicted fluctuations taking into account the method of window averaging performed in Dynamic Mode Decomposition (DMD) analyses. DMD of unsteady flowfield snapshots reveals wave packets of spatially coherent modes having wavelengths and phase speeds characteristic of the acoustic second-mode; their growth and decay occur within the LST-predicted unstable bounds. It was observed that the DSMC-simulated flowfield naturally developed second Mack mode instabilities without any external seeding, i.e., arising spontaneously from the kinetic fluctuations of the simulated gas and of amplitude higher than the predicted DSMC numerical error. Targeted interaction with these flow instabilities is demonstrated for an acoustic vibrating surface (AVS), where forcing at the unstable frequency of 250 kHz results in amplified waves downstream, while at the stable frequency of 400 kHz AVS-induced disturbances are damped. This further emphasizes the ability of the present kinetic simulations to capture and describe linear perturbations at Reynolds numbers corresponding to those of Mach 6 flight at altitudes of $\sim$20 km and suggests that DSMC will be a tool for understanding theoretically-founded study and control of laminar-turbulent transition in hypersonic boundary layers.

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Mert Senkardesler, Irmak T. Karpuzcu, Deborah A. Levin. 2026-09-15. A Kinetic Study of Hypersonic Boundary Layer Second Mack Mode Instabilities. https://arxiv.org/abs/2512.11390

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