Three-Dimensional Rotating Couette Flow Via The Generalised Quasilinear Approximation

TL;DR

This paper evaluates the Generalised Quasilinear (GQL) approximation in three-dimensional rotating Couette flow, showing it significantly improves accuracy over traditional quasilinear models, supporting its use in direct statistical simulations.

Contribution

The study demonstrates that GQL approximation enhances the accuracy of turbulent flow modeling in 3D rotating Couette flow compared to existing quasilinear approaches.

Findings

GQL outperforms QL in predicting mean flows and spectra.

Few modes in GQL suffice for significant accuracy improvements.

Supports GQL's role in direct statistical simulation methods.

Abstract

We examine the effectiveness of the Generalised Quasilinear (GQL) Approximation introduced by Marston et al (2016). This approximation splits the variables into large and small scales in directions where there is a translational symmetry and removes nonlinear interactions involving only small scales. We utilise as a paradigm problem three-dimensional, turbulent, rotating Couette flow. We compare the results obtained from Direct Numerical Solution of the equations with those from Quasilinear (QL) and GQL calculations. In this three-dimensional setting, there is a choice of cut-off wavenumber for the GQL approximation both in the streamwise and in the spanwise directions. We demonstrate that the GQL approximation significantly improves the accuracy of mean flows, spectra and two-point correlation functions over models that are quasilinear in any of the translationally invariant directions, even if only a few streamwise and spanwise modes are included. We argue that this provides significant support for a programme of Direct Statistical Simulation utilising the GQL approximation.