Upstream influence scaling of 2D and 3D shock/turbulent boundary layer interactions at compression corners

The paper considers how the upstream influence of a two-dimensional shock wave/turbulent boundary layer interaction scales with the parameters of the incoming flow. Several recent experiments with equilibrium supersonic, adiabatic turbulent boundary layers are considered in this light. The incoming boundary layer thickness, commonly assumed to be the appropriate scaling parameter for upstream influence, is found to be insufficient for that purpose. Instead the ratio of unit Reynolds number and boundary layer thickness, both raised to fractional powers, is demonstrated to be the appropriate scale. Several candidates for the 'inner deck' length scales are examined for signs of this behavior, but none is found to vary in the same manner as the upstream influence. The upstream influence of a three-dimensional interaction is examined to see if it scales in a manner similar to the two-dimensional interaction. Based on the measurements presented, this is indeed the case, with the important provision that the flow development in both the streamwise and spanwise directions must be scaled simultaneously.