Spatiotemporal representation of the dynamic modes in turbulent cavity flows

Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) were used to extract the coherent structures in turbulent cavity flows. The spatiotemporal representation of the modes was achieved by performing the circular convolution of a change of basis on the data sequence, wherein the transformation function was extracted from the POD or DMD. The spatiotemporal representation of the modes provided significant insight into the evolutionary behavior of the structures. Self-sustained oscillations arise in turbulent cavity flows due to unsteady separation at the leading edge. The turbulent cavity flow at ReD = 12,000 and a length to depth ratio L/D = 2 was analyzed. The dynamic modes extracted from the data clarified the presence of self-sustained oscillations. The spatiotemporal representation of the POD and DMD modes that caused self-sustained oscillations revealed the prevalent dynamics and evolutionary behavior of the coherent structures from their formation at the leading edge to their impingement at the trailing edge. A local minimum in the mode amplitude representing the energy contributions to the flow was observed upon the impingement of coherent structure at the trailing edge. The modal energy associated with the periodic formation of organized coherent structures followed by their dissipation upon impingement revealed the oscillatory behavior over time.