Interaction of forced Orr-Sommerfeld and Squire modes in a low-order representation of turbulent channel flow
A resolvent-based reduced-order representation is used to capture time-averaged second-order statistics in turbulent channel flow. The recently proposed decomposition of the resolvent operator into two distinct families related to the Orr-Sommerfeld and Squire operators [Rosenberg and McKeon, Efficient representation of exact coherent states of the Navier-Stokes equations using resolvent analysis, Fluid Dyn. Res. 51, 011401 (2019)] results in dramatic improvement in the ability to match all components of the energy spectra and the uv cospectrum. The success of the new representation relies on the ability of the Squire modes to compete with the vorticity generated by Orr-Sommerfeld modes, which is demonstrated by decomposing the statistics into contributions from each family. It is then shown that this competition can be used to infer a phase relationship between the two sets of modes. Additionally, the relative Reynolds number scalings for the two families of resolvent weights are derived for the universal classes of resolvent modes presented by Moarref et al. [Moarref, Sharma, Tropp, and McKeon, Model-based scaling of the streamwise energy density in high-Reynolds-number turbulent channels, J. Fluid Mech. 734, 275 (2013)]. These developments can be viewed as a starting point for further modeling efforts to quantify nonlinear interactions in wall-bounded turbulence.
© 2020 American Physical Society. Received 8 January 2020; accepted 1 July 2020; published 18 August 2020. The support of AFOSR under Grant No. FA 9550-16-1-0361 and ONR under Grant No. N00014-17-1-3022 is gratefully acknowledged. Additionally, the authors would like to thank Javier Jiménez for making the spectra for the Re_τ = 934 and 2003 simulations publicly available, as well as Adrián Lozano-Durán for sharing the spectra for Re_τ = 4219.
Submitted - 2001.02785.pdf
Published - PhysRevFluids.5.084607.pdf