PECASE - Multi-Scale Experiments and Modeling in Wall Turbulence

Abstract : A systems approach by which to understand the characteristics and scaling of wall turbulence, resolvent analysis (or critical later framework) has been developed, implemented and reported in a range of archival publications, beginning with McKeon and Sharma [2010]. The approach is in essence a transfer function analysis of the linear Navier-Stokes operator in the streamwise/spanwise wavenumber and temporal frequency space, which identifies and makes use of the low rank nature of this operator in order to achieve order reduction. The outputs have been shown to capture key elements of the turbulence, from statistics to spectral information to arrays of coherent structure. Supporting experiments and modeling have been performed to provide first comprehensive evidence of where in wavenumber-frequency space turbulence activity occurs by characterizing the three-dimensional spectrum of the streamwise velocity fluctuations using time-resolved particle image velocimetry at a range of wall-normal locations, and extending a two-dimensional, three-component model to provide an approximate input mean velocity profile to the analysis. The full resolvent analysis has the potential to provide a self-consistent and self-sustaining model of turbulence, in which the velocity outputs have the correct amplitude and phase to support the appropriate input forcing and (presently assumed) mean velocity profile. Further work is proposed which exploits sparsity in the frequency domain associated with the resolvent formulation to further reduce the complexity of the representation of turbulence and to continue to explore the implications for the scaling of wall turbulence.