Generalised quasilinear approximations of turbulent channel flow: Part 2. Spanwise scale interactions

TL;DR

This paper extends the generalized quasilinear approximation to turbulent channel flow, analyzing spanwise scale interactions and their impact on turbulence dynamics, energy transfer, and statistical features, with implications for modeling turbulence.

Contribution

It introduces a spanwise Fourier mode-based GQL model that captures multi-scale turbulence features and examines the roles of triadic interactions in energy transfer processes.

Findings

GQL models reproduce key statistical features of high-wavenumber turbulence.

Suppression of certain triadic interactions affects energy cascade and inverse transfer.

Inhibition of inverse energy transfer reduces near-wall turbulent transport.

Abstract

Continuing from Part 1 (Hern\'andez \emph{et al.}, \emph{arXiv:2108.12395}, 2021), a generalized quasilinear (GQL) approximation is studied in turbulent channel flow using a flow decomposition defined with spanwise Fourier modes: the flow is decomposed into a set of low-wavenumber spanwise Fourier modes and the rest high-wavenumber modes. This decomposition leads to the nonlinear low-wavenumber group that supports the self-sustaining process within the given integral length scales, whereas the linearised high-wavenumber group is not able to do so, unlike the GQL models in Part 1 which place a minimal mathematical description for the self-sustaining process across all integral scales. Despite the important physical difference, it is shown that the GQL models in this study share some similarities with those in Part 1: i.e. the reduced multi-scale behaviour and anisotropic turbulent fluctuations. Furthermore, despite not being able to support the self-sustaining process in the high-wavenumber group, the GQL models in the present study are found to reproduce some key statistical features in the high-wavenumber group solely through the `scattering' mechanism proposed by previous studies. Finally, using the nature of the GQL approximation, a set of numerical experiments suppressing certain triadic nonlinear interactions are further carried out. This unveils some key roles played by the certain types of triadic interactions including energy cascade and inverse energy transfer in the near-wall region. In particular, the inhibition of inverse energy transfer in the spanwise direction leads to suppression of the near-wall positive turbulent transport at large scales.