Dynamic Mode Decomposition Analysis of Separated Boundary Layers Under Variable Reynolds Number and Free-Stream Turbulence

Abstract A flat plate boundary layer has been surveyed by means of time-resolved particle image velocimetry (PIV) under variable Reynolds number (70000 < Re < 150000) and turbulence intensity level (1.5% < Tu < 2.5%). The PIV visualizations were completed in two measuring planes, that are oriented both normal and parallel to the wall. For the wall-parallel configuration, the measuring plane is located inside the boundary layer. The PIV data were post-processed by applying Dynamic Mode Decomposition (DMD), which provides frequency based modes and their corresponding growth rate. The effects of Re and Tu variation on the amplification of the dominant wavelength within the separated shear layer, which is responsible for transition, is the main subject of the present work. The DMD modes and related eigenvalues were computed with reference to the main streamwise coordinate. This allowed discussing the effects due to the main flow parameters on the amplification of the dominant streamwise wavelengths within the separated shear layer (Kelvin-Helmholtz modes). The growth of such streamwise modes ends with the formation of large scale vortices, whose breakup forces transition. In order to obtain the effective distribution of the maximum growth rate of fluctuations at different locations and times, the DMD domain was continuously extended in the streamwise direction, accounting for a specified number of periods characterizing the large scale K-H vortices. In order to reduce the time-space dependent results obtained by the DMD procedure, a probability density function of the most unstable wavelength and the corresponding growth rate has been computed. For the present data set, the spatial growth rate of fluctuations is found to increase at the higher Reynolds number, while it slightly reduces with increasing the Tu level. The procedure and findings discussed in this work shall be suitable for designing active control systems, such as harmonic blowing for separation control.