Free-stream disturbance receptivity and amplification at hypersonic speeds by adjoint Green’s function

Transition to turbulence in the boundary layer on hypersonic vehicles in flight is difficult to infer from wind tunnel tests or at reasonable computational cost.

A new physically motivated scaling for transition location on blunt cones in tunnel tests is shown to collapse several experimental datasets in the absence of transition reversal. This scaling supports transient growth as the transition mechanism, even when approaching the sharp limit, contrary to traditional wisdom.

The discrepancy between transition in flight and in tunnel tests is addressed by answering the question of how fluctuations in the free-stream are transported into the boundary layer and amplified on a blunt cone. The receptivity and amplification of a disturbance that arrives at a point near transition is directly computed by way of the adjoint Green’s function. The adjoint Green’s function provides a quantitative account of all possible linear receptivity and amplification mechanisms in a way that is agnostic to a particular choice of free-stream disturbance field.