The colour of forcing statistics in resolvent analyses of turbulent channel flows

Abstract

Abstract

Forcing statistics in resolvent analysis: application in minimal turbulent Couette flow

“…A recent example is found in Morra et al. (2020), where the nonlinear forcing was shown to be rank-2 for the most energetic frequencies of channel flows at moderate Reynolds numbers (), suggesting that, even though the forcing may not be low rank over all frequencies, it has low rank for the most dynamically important frequencies of the flow. In the present Couette flow, despite the apparent complexity of the bulk of nonlinear terms, order can still be found.…”

“…Even though nonlinear forcings are not expected to be low rank over all frequencies and wavenumbers, especially in higher-Reynolds-number flows, the present analysis suggests that orderly structures in the forcing terms may still be found, and these can be particularly important in the dynamics of turbulent flows, such as in the self-sustained process in wall-bounded flows. A recent example is found in Morra et al (2020), where the nonlinear forcing was shown to be rank-2 for the most energetic frequencies of channel flows at moderate Reynolds numbers (Re τ = 180, 550), suggesting that, even though the forcing may not be low rank over all frequencies, it has low rank for the most dynamically important frequencies of the flow. In the present Couette flow, despite the apparent complexity of the bulk of nonlinear terms, order can still be found.…”

Resolvent-based optimal estimation of transitional and turbulent flows

“…We now consider a turbulent channel flow with friction Reynolds number Re τ = 180. We use data obtained via direct numerical simulation (DNS) to compute the flow and nonlinear forcing statistic, both of which were previously documented by Morra (2020) and Morra et al (2020), to compare with our estimation results. Inner (viscous) units can be defined in terms of a friction velocity u τ = √ τ w /ρ, where τ w is the mean wall shear and ρ the fluid density.…”

Ambiguity in mean-flow-based linear analysis

“…This is counter-intuitive since the alignment of SPOD and resolvent modes is often associated with high gain separation in the resolvent operator (Beneddine et al 2016), considering that the nonlinear terms are close to white noise and thus have similar projection coefficients onto the forcing mode basis. However, the presence of coherent low-rank forcing, as recently observed for turbulent channel flow (Morra et al 2020), may change this picture. The overall weight of a response mode inq is determined by the corresponding gain together with the projection of the actual forcing,f on to the corresponding forcing mode of the resolvent operator.…”