A Three-Dimensional Extension of Minimal Quasi-Linear Approximation for Channel Flow
Abstract
This paper extends a minimal quasi-linear approximation proposed in Hwang and Eckhardt to account for turbulent channel flow. A data-driven approach is applied to determine the optimal stochastic forcing for a linearized, eddy-viscosity based model. The streamwise forcing distribution is determined through an optimization problem, matching the two-dimensional spectra from a DNS at Reτ = 5200 to the linearised response, with the forcing subject to sufficient smoothness. Results are determined for fixed spanwise lengthscales and the self-similarity of energy-containing motions throughout the near-wall and logarithmic regions is exploited to determine a universal distribution. The spanwise forcing distribution is then determined self-consistently by matching the spanwise forcing distribution such that the Reynolds stress produced from the fluctuations matches that from the eddy-viscosity based mean flow. The two-dimensional spectra and turbulence intensities and quasi-linear approximation are then compared, with improvement found over the anisotropic previous results, qualitatively consistent with energetics of the self-sustaining process.
- Publication:
-
APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- 2020
- Bibcode:
- 2020APS..DFDS10019H