Second-mode Waves in Hypersonic Boundary Layers: Energy Balance, Kinematics and Mechanics

This study explores the influence of wall temperature on second-mode instabilities during hypersonic boundary layer transition. Direct numerical simulations (DNS), supported by linear stability theory, are conducted over a sharp cone in Mach 6 flow. A second-order disturbance energy equation, closed using DNS data, reveals the mechanisms of energy production and transport that drive instability growth. Results show that second-mode waves behave as trapped acoustic disturbances, with trapping enhanced under colder wall conditions due to stronger velocity gradients. Energy production relies on in-phase velocity and temperature fluctuations at the inflection line, with energy transported downward to sustain near-wall pressure fluctuations. Phase relationships are crucial: a ninety-degree phase difference between pressure and wall-normal velocity indicates standing wave formation. Colder walls maintain the phase structure needed for strong coupling and resonance, promoting instability growth. In contrast, heated walls disrupt this phasing, stabilizing the flow. Nonlinear effects eventually limit growth, leading to energy saturation.