Multiscale and Directional Approach to Rotating Shear Flow

Zhu, Ying; Cambon, Claude; Godeferd, Fabien S.

doi:10.1007/978-3-030-42822-8_50

Cited by 2 publications

(2 citation statements)

References 10 publications

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“…The results in Figure 4 (and other results at different wave numbers and for various values of R in [14]) show clearly an almost perfect coincidence between the SO(3) type decomposition and the SSH expansion.…”

Section: (Dir) Ijsupporting

confidence: 62%

“…ZCG is a statistical spectral model developed for homogeneous anisotropic turbulence by the author Y. Zhu, C. Cambon, and our collaborator F. S. Godeferd. For all relevant formulas, numerical details, and simulation results presented in this section, part of them are published in Zhu et al (2019) [6], and the other unpublished part is in the Ph.D. thesis of the first author [14].…”

Section: Recalling Zcg Modelmentioning

confidence: 99%

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Modal Projection for Quasi-Homogeneous Anisotropic Turbulence

Zhu

Cambon

2023

Atmosphere

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This article, or essay, addresses the anisotropic structure and the dynamics of quasi-homogeneous, incompressible turbulence. Modal projection and expansions in terms of spherical harmonics in three-dimensional Fourier space are in line with a seminal study by Jack Herring, around the so-called Craya–Herring frame of reference, with a large review of the related approaches to date. The research part is focused on structure and dynamics of rotating sheared turbulence, including a description of both directional and polarization anisotropy with a minimal number of modes. Effort is made to generalize expansions in terms of scalar spherical harmonics (SSHs) to vector spherical harmonics (VSHs). Looking at stochastic fields, for possibly intermittent vector fields, some directions are explored to reconcile modal projection, firstly used for smooth vector fields, and multifractal approaches for internal intermittency but far beyond scalar correlations, such as structure functions. In order to illustrate turbulence from Earth to planets, stars, and galaxies, applications to geophysics and astrophysics are touched upon, with generalization to coupled vector fields (for kinetic, magnetic, and potential energies), possibly dominated by waves (Coriolis, gravity, and Alfvén).

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Section: (Dir) Ijsupporting

confidence: 62%

Section: Recalling Zcg Modelmentioning

confidence: 99%

Modal Projection for Quasi-Homogeneous Anisotropic Turbulence

Zhu

Cambon

2023

Atmosphere

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Nonlinear spectral model for rotating sheared turbulence

et al. 2019

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We propose a statistical model for homogeneous turbulence undergoing distortions, which improves and extends the MCS model by Mons, Cambon & Sagaut (J. Fluid Mech., vol. 788, 2016, 147–182). The spectral tensor of two-point second-order velocity correlations is predicted in the presence of arbitrary mean-velocity gradients and in a rotating frame. For this, we numerically solve coupled equations for the angle-dependent energy spectrum ${\mathcal{E}}(\boldsymbol{k},t)$ that includes directional anisotropy, and for the deviatoric pseudo-scalar $Z(\boldsymbol{k},t)$, that underlies polarization anisotropy ($\boldsymbol{k}$ is the wavevector, $t$ the time). These equations include two parts: (i) exact linear terms representing the viscous spectral linear theory (SLT) when considered alone; (ii) generalized transfer terms mediated by two-point third-order correlations. In contrast with MCS, our model retains the complete angular dependence of the linear terms, whereas the nonlinear transfer terms are closed by a reduced anisotropic eddy damped quasi-normal Markovian (EDQNM) technique similar to MCS, based on truncated angular harmonics expansions. And in contrast with most spectral approaches based on characteristic methods to represent mean-velocity gradient terms, we use high-order finite-difference schemes (FDSs). The resulting model is applied to homogeneous rotating turbulent shear flow with several Coriolis parameters and constant mean shear rate. First, we assess the validity of the model in the linear limit. We observe satisfactory agreement with existing numerical SLT results and with theoretical results for flows without rotation. Second, fully nonlinear results are obtained, which compare well to existing direct numerical simulation (DNS) results. In both regimes, the new model improves significantly the MCS model predictions. However, in the non-rotating shear case, the expected exponential growth of turbulent kinetic energy is found only with a hybrid model for nonlinear terms combining the anisotropic EDQNM closure and Weinstock’s return-to-isotropy model.

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Multiscale and Directional Approach to Rotating Shear Flow

Cited by 2 publications

References 10 publications

Modal Projection for Quasi-Homogeneous Anisotropic Turbulence

Modal Projection for Quasi-Homogeneous Anisotropic Turbulence

Nonlinear spectral model for rotating sheared turbulence

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