Yongyun Hwang (Imperial College): An optimisation-based quasi-linear approximation for shear flows
Channel: UKFN SIG Flow instability, modelling and control
Date: 2020-06-19

This is one of the talks of the 1st online meeting of the UKFN SIG on Flow Instability Modelling and Control (27/05/2020). Full details of the event are available at https://fluids.ac.uk/sig/FlowInstability

SPEAKER: Yongyun Hwang, Imperial College (with Bruno Eckhardt)

TITLE: An optimisation-based quasi-linear approximation for linearly stable shear flows: application to turbulent channel flow up to Re_tau=20,000.

ABSTRACT: A quasi-linear approximation for linearly stable mean flow is proposed and applied to turbulent channel flow. The velocity field is decomposed into a mean profile and fluctuations. While the mean is obtained from the nonlinear equations, the fluctuations are modelled by replacing the nonlinear self-interaction terms with an eddy-viscosity-based turbulent diffusion and stochastic forcing. The stochastic forcing is then determined self-consistently by solving an optimisation problem which minimises the difference between the Reynolds shear stresses from the mean and fluctuation equations, subject to a constraint that the averaged Reynolds shear-stress spectrum is sufficiently smooth in the spatial wavenumber space. The proposed quasi-linear approximation is subsequently applied to channel flow for Reynolds number Re_tau ranging from 500 to 20,000. The best result is obtained when the Reynolds stress is calculated by retaining only the two leading POD (proper orthogonal decomposition) modes, which further filters out the modelling artifact caused by the unphysical stochastic forcing. In this case, the resulting turbulence intensity profile and energy spectra exhibit the same qualitative behaviour as DNS data throughout the entire wall-normal domain, while reproducing the classical predictions made by Townsend (1956).