Energetic pathways to non-adiabatic Görtler laminar to turbulent transition

Large eddy simulations of Görtler instability in a subsonic flow are used to investigate the influence of non-adiabatic walls. The analysis employs an intermediate Non-Oberbeck–Boussinesq framework and a novel inter-modal energy transfer decomposition. Active wall temperature is shown to dictate two distinct architectural pathways to turbulence. The heated wall exhibits a dual-regime transition, beginning with coherent Görtler vortex that break down via a varicose mode, and an emerging secondary vortex regime, energized by high momentum freestream fluid during the ejection-sweep mechanism, later terminates via an inner sinuous mode. This study tracks the energetic pathway for the formation and evolution of both regimes, revealing a twisting mode in the spanwise-wall normal plane that channels energy between the dynamic coherent Görtler vortex and the secondary vortex regime. In contrast, the cooled wall follows a protracted, single-regime transition stabilized by buoyancy, whereas the aforementioned secondary vortex regime is completely suppressed. Mechanistically, buoyancy is found to influence Görtler transition through the homogeneous isotropic deformation of the base state and the anisotropic modulation of turbulent production. In the cooled wall case, the structural confinement imposed by homogeneous contraction acts as the dominant stabilizing force, overriding local anisotropic effects to strictly delay transition. Conversely, wall heating induces a complex interaction: homogeneous expansion structurally destabilizes the primary Görtler vortex, accelerating the varicose mode dominance and breakdown, while local anisotropic stabilization acts selectively to sustain the ejection-sweep cycle that fuels the secondary Görtler vortex regime.