M. Grilli, P.J. Schmidt, S. Hickel, N.A. Adams (2012)
Journal of Fluid Mechanics 700: 16-28. doi: 10.1017/jfm.2012.37

The unsteady behaviour in shockwave turbulent boundary layer interaction is investigated by analysing results from a large eddy simulation of a supersonic turbulent boundary layer over a compression–expansion ramp. The flow dynamics are analysed by a dynamic mode decomposition which shows the presence of a low-frequency mode associated with the pulsation of the separation bubble and accompanied by a forward–backward motion of the shock.

The interaction leads to a very-low-frequency motion near the foot of the shock, with a characteristic frequency that is three orders of magnitude lower than the typical frequency of the incoming boundary layer.  Wall pressure data are analysed by means of Fourier analysis, highlighting the low-frequency phenomenon in the interaction region. 


Reconstruction of the glow field based on four DMD modes. The solid black line is the instantaneous shock position, the dashed black line is the mean shock location. The recirculation bubble is visualized by streamlines (thin black lines) and the red dashed line is one streamline of the mean flow.


Reconstruction of the temporal evolution of (a) mass of the reverse-flow region and (b) shock location based on one to four DMD modes.