Global stability analyses of Mack mode on the windward face of a hypersonic yawed cone

Steady laminar flow over a blunt cone at 5 degrees angle of attack has been computed at Mach number 6 and unit Reynolds number Re*infinity = 2.079 x 107 m-1. The flow condi-tions are selected to match the flight test conducted by China Aerodynamics Research and Development Center at an altitude of 16 km where windward-side boundary-layer transition was detected. In order to understand the underlying transition mechanisms, we perform local and global stability analyses, focusing on linear and nonlinear stability characteristics of Mack-mode instability which prevails in the windward side. The global instability spectrum contains two distinct types of modes: few isolated eigenmodes (branch D) lying in the vicinity of the windward ray, and an arc branch (branch S) of eigenmodes in the outboard region. D modes originate in branch S and are considerably more unstable than S modes, potentially causing an indented transition front. Nonlinear development of a single symmetric D mode that inherently contains broadband oblique components will inevitably trigger the fundamental resonance without additional perturbations, once the mode temperature amplitude exceeds 10% of the free-stream value; moreover, the combination resonance is subordinate to the fundamental resonance as the latter always occurs prior to the former. The antisymmetric D mode is less amplified than the symmetric counterpart, yet it is still able to rapidly broaden the azimuthal wave-number spectrum through triad interactions among oblique components. In either case, the global primary mode is found to act as a catalyst to promote rapid amplifications of certain oblique components that ultimately lead to streaky structures in the vicinity of the windward ray. The streaks in turn are significantly unstable to low-frequency waves that are likely responsible for the final breakdown.