Distorted turbulence submitted to frame rotation: RDT and LES results

The objective of this effort is to carry the analysis of Lee et al. (1990) to the case of shear with rotation. We apply the RDT approximation to turbulence submitted to frame rotation for the case of a uniformly sheared flow and compare its mean statistics to results of high resolution DNS of a rotating plane channel flow. In the latter, the mean velocity profile is modified by the Coriolis force, and accordingly, different regions in the channel can be identified. The properties of the plane pure strain turbulence submitted to frame rotation are, in addition, investigated in spectral space, which shows the usefulness of the spectral RDT approach. This latter case is investigated here. Among the general class of quadratic flows, this case does not follow the same stability properties as the others since the related mean vorticity is zero

On the effect of rotation on magnetohydrodynamic turbulence at high magnetic Reynolds number

This article is focused on the dynamics of a rotating electrically conducting fluid in a turbulent state. As inside the Earth's core or in various industrial processes, a flow is altered by the presence of both background rotation and a large scale magnetic field. In this context, we present a set of 3D direct numerical simulations of incompressible decaying turbulence. We focus on parameters similar to the ones encountered in geophysical and astrophysical flows, so that the Rossby number is small, the interaction parameter is large, but the Elsasser number, defining the ratio between Coriolis and Lorentz forces, is about unity. These simulations allow to quantify the effect of rotation and thus inertial waves on the growth of magnetic fluctuations due to Alfv\'en waves. Rotation prevents the occurrence of equipartition between kinetic and magnetic energies, with a reduction of magnetic energy at decreasing Elsasser number {\Lambda}. It also causes a decrease of energy transfer mediated by cubic correlations. In terms of flow structure, a decrease of {\Lambda} corresponds to an increase in the misalignment of velocity and magnetic field.Comment: 18 pages, 12 figure

Magnetized stratified rotating shear waves

International audienceWe present a spectral linear analysis in terms of advected Fourier modes to describe the behavior of a fluid submitted to four constraints: shear (with rate S), rotation (with angular velocity Ω), stratification, and magnetic field within the linear spectral theory or the shearing box model in astrophysics. As a consequence of the fact that the base flow must be a solution of the Euler-Boussinesq equations, only radial and/or vertical density gradients can be taken into account. Ertel's theorem no longer is valid to show the conservation of potential vorticity, in the presence of the Lorentz force, but a similar theorem can be applied to a potential magnetic induction: The scalar product of the density gradient by the magnetic field is a Lagrangian invariant for an inviscid and nondiffusive fluid. The linear system with a minimal number of solenoidal components, two for both velocity and magnetic disturbance fields, is eventually expressed as a four-component inhomogeneous linear differential system in which the buoyancy scalar is a combination of solenoidal components (variables) and the (constant) potential magnetic induction. We study the stability of such a system for both an infinite streamwise wavelength (k1=0, axisymmetric disturbances) and a finite one (k1≠0, nonaxisymmetric disturbances). In the former case (k1=0), we recover and extend previous results characterizing the magnetorotational instability (MRI) for combined effects of radial and vertical magnetic fields and combined effects of radial and vertical density gradients. We derive an expression for the MRI growth rate in terms of the stratification strength, which indicates that purely radial stratification can inhibit the MRI instability, while purely vertical stratification cannot completely suppress the MRI instability. In the case of nonaxisymmetric disturbances (k1≠0), we only consider the effect of vertical stratification, and we use Levinson's theorem to demonstrate the stability of the solution at infinite vertical wavelength (k3=0): There is an oscillatory behavior for τ>1+∣∣K2/k1∣∣, where τ=St is a dimensionless time and K2 is the radial component of the wave vector at τ=0. The model is suitable to describe instabilities leading to turbulence by the bypass mechanism that can be relevant for the analysis of magnetized stratified Keplerian disks with a purely azimuthal field. For initial isotropic conditions, the time evolution of the spectral density of total energy (kinetic + magnetic + potential) is considered. At k3=0, the vertical motion is purely oscillatory, and the sum of the vertical (kinetic + magnetic) energy plus the potential energy does not evolve with time and remains equal to its initial value. The horizontal motion can induce a rapid transient growth provided K2/k1≫1. This rapid growth is due to the aperiodic velocity vortex mode that behaves like Kh/kh where kh(τ)=[k21+(K2−k1τ)2]1/2 and Kh=kh(0). After the leading phase (τ>K2/k1≫1), the horizontal magnetic energy and the horizontal kinetic energy exhibit a similar (oscillatory) behavior yielding a high level of total energy. The contribution to energies coming from the modes k1=0 and k3=0 is addressed by investigating the one-dimensional spectra for an initial Gaussian dense spectrum. For a magnetized Keplerian disk with a purely vertical field, it is found that an important contribution to magnetic and kinetic energies comes from the region near k1=0. The limit at k1=0 of the streamwise one-dimensional spectra of energies, or equivalently, the streamwise two-dimensional (2D) energy, is then computed. The comparison of the ratios of these 2D quantities with their three-dimensional counterparts provided by previous direct numerical simulations shows a quantitative agreement

From baroclinic instability to developed turbulence

The coupled effects of mean shear, density-stratification and system rotation are investigated in the context of strong turbulence, i.e. accounting for the baroclinic instability. Although there exists a large literature in the rotating shear case and the stratified shear case, with linear approaches, Direct or Large Eddy Simulations, very few studies consider the combined three ingredients in the context of distorted homogeneous turbulence

Etude des propriétés de la turbulence confinée en rotation à l'aide d'une méthode de pénalisation

Ce travail numérique porte sur l'étude de l'influence globale du confinement sur la turbulence. On montre, que ce soit sur le comportement Eulérien ou Lagrangien de la turbulence, que la distance à la paroi est d'une importance essentielle dans la description statistique de tels écoulements. On utilise un code pseudo-spectral tri-périodique dans lequel est implémenté une méthode de pénalisation, permettant de prendre en compte la présence de parois solides. On utilise également cette méthode pour considérer des parois mobiles afin de limiter le déclin de l'énergie cinétique

On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence

We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasi-static approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of component along the magnetic field [Moffatt, JFM 28, 1967]. However, numerous numerical studies predict a different behaviour, wherein the final state is characterized by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using Direct Numerical Simulations. The initial temporal evolution of the decaying flow indicates that the turbulence is very similar to the so-called "two-and-a-half-dimensional" flow [Montgomery & Turner, Phys. Fluids 25(2), 1982] and we offer an explanation for the dominance of horizontal kinetic energy.Comment: 17 pages, 8 figure

Phase-mixing and toroidal cascade in rotating and stratified flows

We study anisotropic statistics in rotating stratified flows. The toroidal/poloidal decomposition exhibits two limits: 2D modes with horizontal wavevectors, and 1D vertically sheared horizontal modes, with only vertical wavevectors. For rotation, both toroidal and poloidal components are affected by inertial waves, thus anisotropic phase mixing is responsible for transient effects, whereas resonant triads control the long-term dynamics. We compare the development of triple vorticity correlations by pure linear theory, statistical EDQNM theory, experiments and DNS. The dominance of cyclonic vertical vorticity is explained without instabilities arguments. For stable stratification, strong nonlinearity only affects the pure toroidal mode, whereas any interaction involving the poloidal mode deals with weak gravity-wave turbulence. We then explore the toroidal cascade. We show its consistency with a spherical shell-to-shell direct cascade. It can explain the angular energy drain from quasi-2D modes to quasi-1D VSHF modes, which quantifies the horizontal layering of the flow, again without advocating instability mechanisms

Relating statistics to dynamics in axisymmetric homogeneous turbulence

The structure and the dynamics of homogeneous turbulence are modified by the presence of body forces such that the Coriolis or the buoyancy forces, which may render a wide range of turbulence scales anisotropic. The corresponding statistical characterization of such effects is done in physical space using structure functions, as well as in spectral space with spectra of two-point correlations, providing two complementary viewpoints. In this framework, second-order and third-order structure functions are put in parallel with spectra of two-point second- and third-order velocity correlation functions, using passage relations. Such relations apply in the isotropic case, or for isotropically averaged statistics, which, however, do not reflect the actual more complex structure of anisotropic turbulence submitted to rotation or stratification. This complexity is demonstrated in this paper by orientation-dependent energy and energy transfer spectra produced in both cases by means of a two-point statistical model for axisymmetric turbulence. We show that, to date, the anisotropic formalism used in the spectral transfer statistics is especially well-suited to analyze the refined dynamics of anisotropic homogeneous turbulence, and that it can help in the analysis of isotropically computed third-order structure function statistics often used to characterize anisotropic contexts.Comment: Physica

Flow dynamics and magnetic induction in the von-Karman plasma experiment

The von-Karman plasma experiment is a novel versatile experimental device designed to explore the dynamics of basic magnetic induction processes and the dynamics of flows driven in weakly magnetized plasmas. A high-density plasma column (10^16 - 10^19 particles.m^-3) is created by two radio-frequency plasma sources located at each end of a 1 m long linear device. Flows are driven through JxB azimuthal torques created from independently controlled emissive cathodes. The device has been designed such that magnetic induction processes and turbulent plasma dynamics can be studied from a variety of time-averaged axisymmetric flows in a cylinder. MHD simulations implementing volume-penalization support the experimental development to design the most efficient flow-driving schemes and understand the flow dynamics. Preliminary experimental results show that a rotating motion of up to nearly 1 km/s is controlled by the JxB azimuthal torque