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

Abstract

Continuing from Part 1 (Hernández et al., J. Fluid Mech., vol. 936, 2022, A33), a generalised 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 further set of numerical experiments suppressing certain triadic nonlinear interactions are carried out. This unveils some key roles played by 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.

Separating large-scale superposition and modulation in turbulent channels

“…While the latter observation is in line with the evidence of a small-to-large energy transfer in the near-wall region found by Cho et al (2018), Jacobi et al (2021) and Hernández et al (2022), the results yielded by suppression of superposition show that the present understanding of amplitude modulation is still only partial. Our results do not exclude that, for instance, the large-scale velocity gradient may locally have a modulating action on small-scale activity as proposed by Agostini & Leschziner (2019a); moreover, the ansatz that near-wall small scales are locally modulated by near-wall large scales (for instance, Zhang & Chernyshenko 2016) can still be a starting point for models that yield satisfactory results, owing to the spatial coherence of the large scales.…”

“…(2022). Exploiting a generalised quasi-linear approximation of a turbulent channel flow, Hernández, Yang & Hwang (2022) also support the idea that small-scale fluctuations may be involved in large-scale generation mechanisms. They found that the inhibition of particular triadic interactions involved in inverse energy transfer in the spanwise direction within the near-wall region led to suppression of the near-wall positive turbulent transport at large scales.…”

A data-driven quasi-linear approximation for turbulent channel flow

“…2016; Hernández et al. 2022 a , b ). Lastly, the present DQLA employs a steady-state stochastic dynamical systems framework, overlooking any time/frequency domain details.…”

可压缩壁湍流物理与建模研究进展

“…By simplifying the forcing representation, Thomas et al [246] proposed the restricted nonlinear model (RNL) of lower computational cost (see the summary of Farrell et al [247]). More recent progress on these quasilinear models can be found in, e.g., Tobias and Marston [248] and Hernández et al [249,250].…”