Global modal/non-modal analysis of high-enthalpy Martian entry vehicles

Abstract: We analyze laminar-to-turbulent transition over a blunt capsule representative of Martian entry at Mach 26 using global modal and transient-growth analyses about a thermochemical base flow characteristic of high-altitude entry conditions. Across the Reynolds-number range considered ($Re_\infty = 10<sup>4$--$10^6$), the axisymmetric global eigenspectrum remains stable, ruling out temporally unstable axisymmetric global modes as a viable route to transition. The flow nevertheless supports strong transient growth concentrated in the shear--entropy layer generated by bow-shock curvature. Energy-budget analysis reveals a two-stage process: Reynolds-stress production in the mean shear first amplifies kinetic disturbances, which then generate entropy fluctuations as they traverse the strong base-flow entropy gradient. The optimal gain scales linearly with the Reynolds number based on the capsule nose radius, whereas boundary-layer-localized disturbances become competitive at the highest Reynolds numbers examined. These results identify shear--entropy-layer transient growth as a plausible linear pathway for seeding transition in high-enthalpy blunt-entry vehicles.