Spectral Energetics of a Quasilinear Approximation in Uniform Shear Turbulence

Abstract

The spectral energetics of a quasilinear (QL) model is studied in uniform shear turbulence. For the QL approximation, the velocity is decomposed into a mean averaged in the streamwise direction and the remaining fluctuation. The equations for the mean are fully considered, while the equations for the fluctuation are linearised around the mean. The QL model exhibits an energy cascade in the spanwise direction, but this is mediated by highly anisotropic small-scale motions unlike that in direct numerical simulation mediated by isotropic motions. In the streamwise direction, the energy cascade is shown to be completely inhibited in the QL model, resulting in highly elevated spectral energy intensity residing only at the streamwise integral length scales. It is also found that the streamwise wavenumber spectra of turbulent transport, obtained with the classical Reynolds decomposition, statistically characterizes the instability of the linearised fluctuation equations. Further supporting evidence of this claim is presented by carrying out a numerical experiment, in which the QL model with single streamwise Fourier mode is found to generate the strongest turbulence for L x /L z = 1 ∼ 3, consistent with previous findings (L x and L z are the streamwise and spanwise computational domains, respectively). Finally, the QL model is shown to completely ignore the role of slow pressure in the fluctuations, resulting in a significant damage of pressure-strain transport at all length scales. This explains the anisotropic turbulence of the QL model throughout the entire wavenumber space as well as the inhibited nonlinear regeneration of streamwise vortices in the self-sustaining process. * x,z,t = 1,(2.15a) * 10 −3 and −Φ uv * 10 −4 . This is in sharp contrast to the spectra of QL model. First of all,

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

“…From the incompressibility of the given fluid, the pressure strain terms satisfy the relation further discussion on this can be found in previous studies (Mizuno 2016; Cho et al. 2018; Lee & Moser 2019; Hernández & Hwang 2020; Hernández et al. 2022).…”

“…A large eddy simulation (LES) is first carried out with the numerical solver used in Part 1 (Hernández & Hwang 2020). The main difference of the simulation in the present study from that in Part 1 is the computational domain size.…”

“…2017; Pausch et al. 2019; Hernández & Hwang 2020) and generalised quasilinear approximations (GQL) (Constantinou 2015; Marston et al. 2016; Tobias & Marston 2017).…”

“…2019; Hernández & Hwang 2020); in the QL model, the elongated streaks are captured by the nonlinear streamwise mean equations, and the streamwise wavy instability by the linearised equations. The recent examination of this model in uniform shear turbulence (Hernández & Hwang 2020) revealed that the inhibition of the streamwise energy cascade in the QL model by construction results in highly elevated spectral energy intensity residing only at the streamwise integral length scale, and consequently, only a small number of streamwise Fourier modes remain active (Thomas et al. 2014, 2015; Farrell et al.…”

“…2017; Pausch et al. 2019; Hernández & Hwang 2020), which offers the dynamics of the energy-containing streamwise waves in a minimal manner. In Part 1 (Hernández et al.…”