Nonmodal instabilities along the leeward side of a high-speed yawed circular cone

Recent studies have revealed exceptionally low transition N-factors (below 2) based on modal instabilities for the leeward ray of yawed cones in the wind tunnels, suggesting that nonmodal growth mechanisms could potentially play a significant role. In light of these findings, the present work employs optimal growth theory to examine linear evolution of optimal disturbances on the leeward side of cones at 2° and 4° angles of attack in high-speed flows. Three distinct types of optimal disturbances are identified: low-frequency disturbance, Mack-mode-like disturbance, and entropy-layer disturbance. Among these, low-frequency disturbances exhibit the highest N-factors of approximately 5.5 near experimentally observed transition locations. Aside from the entropy-layer disturbance which relies solely on the Orr mechanism, the other optimal disturbances initially leverage the lift-up or Orr mechanism and progressively transition to growth driven by the modal instability mechanism downstream. The dominant energy production for all three types of disturbances mainly comes from the wall-normal shear of the base flow. Specifically, the low-frequency and Mack-mode-like disturbances gain energy inside the boundary layer, whereas the entropy-layer disturbance obtains its energy within the entropy layer region outside the boundary layer.