Spectral Proper Orthogonal Decomposition of Unsteady Wall Shear Stress Under a Turbulent Separation Bubble

Spectral proper orthogonal decomposition (SPOD) is used to investigate the low-frequency behavior of a pressure-induced turbulent separation bubble (TSB) generated on a one-sided diffuser at a nominal velocity of 20 m/s. The input to the decomposition is the unsteady wall shear stress determined experimentally with an array of novel calorimetric shear-stress sensors. The SPOD spectrum indicates low-rank behavior for frequencies below 10 Hz, which correspond to Strouhal numbers [Formula: see text] when built with the average TSB length and the nominal incoming velocity. A low-order model constructed with only the first SPOD mode at each frequency up to 10 Hz reveals that the TSB is contracting and expanding in a manner reminiscent of the low-frequency breathing motion recently documented in other TSBs. A comparison between SPOD and space-only proper orthogonal decomposition (POD) indicates that both decompositions are able to capture the low-frequency breathing motion as long as space-only POD is applied on signals previously low-pass filtered at 10 Hz. However, the superiority of SPOD is revealed by its inherent capacity to express the frequency range amenable to low-rank behavior. In addition to offering new insights into the low-frequency dynamics of TSBs, the present results also demonstrate the usefulness of calorimetric shear-stress sensors for the study of turbulent separating and reattaching flows.