On low-frequency unsteadiness in swept shock wave–boundary layer interactions

We derive a scaling law for the characteristic frequencies of wall pressure fluctuations
in swept shock wave/turbulent boundary layer interactions in the presence of cylindrical
symmetry, based on analysis of a direct numerical simulations database. Direct numerical
simulations in large domains show evidence of spanwise rippling of the separation line,
with typical wavelength proportional to separation bubble size. Pressure disturbances
around the separation line are shown to be convected at a phase speed proportional
to the cross-flow velocity. This information is leveraged to derive a simple model for
low-frequency unsteadiness, which extends previous two-dimensional models (Piponniau
et al., J. Fluid Mech., vol. 629, 2009, pp. 87–108), and which correctly predicts growth of
the typical frequency with the sweep angle. Inferences regarding the typical frequencies in
more general swept shock wave/turbulent boundary layer interactions are also discussed.