Earliest transition Reynolds number in hypersonic boundary layers

An ensemble-variational algorithm is developed to establish strict bounds on transition Reynolds number in high-speed boundary layers, for specified level of free-stream disturbance energy. The formulation is a constrained optimization where the spectral makeup of the nonlinearly most dangerous disturbance is the control variable, and the constraint is its energy. The optimal amplitudes and phases of the constituent waves cause the earliest possible breakdown to turbulence. Transition is examined in a flat-plate boundary layer at Mach = 4.5, when the energy level is of the same order as that of stratospheric turbulence. The nonlinearly most dangerous disturbance leads to a unique transition mechanism that cannot be categorized as classical fundamental or oblique breakdown. Breakdown to turbulence is initiated due to nonlinear interactions of two acoustic waves and an oblique vorticity wave. The analysis, repeated at different levels of free-stream disturbance energy, provides strict bounds on transition Reynolds numbers.