Large-scale anisotropy in stably stratified rotating flows

We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to $1024^3$ grid points and Reynolds numbers of $\approx 1000$. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with $\sim k_\perp^{-5/3}$, including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales

Inverse cascades and resonant triads in rotating and stratified turbulence

Kraichnan’s seminal ideas on inverse cascades yielded new tools to study common phenomena in geophysical turbulent flows. In the atmosphere and the oceans, rotation and stratification result in a flow that can be approximated as two-dimensional at very large scales but which requires considering three-dimensional effects to fully describe turbulent transport processes and non-linear phenomena. Motions can thus be classified into two classes: fast modes consisting of inertia-gravity waves and slow quasi-geostrophic modes for which the Coriolis force and horizontal pressure gradients are close to balance. In this paper, we review previous results on the strength of the inverse cascade in rotating and stratified flows and then present new results on the effect of varying the strength of rotation and stratification (measured by the inverse Prandtl ratio N/f, of the Coriolis frequency to the Brunt-Väisäla frequency) on the amplitude of the waves and on the flow quasi-geostrophic behavior. We show that the inverse cascade is more efficient in the range of N/f for which resonant triads do not exist, /2≤N/f≤21/2≤N/f≤2. We then use the spatio-temporal spectrum to show that in this range slow modes dominate the dynamics, while the strength of the waves (and their relevance in the flow dynamics) is weaker.Fil: Oks, D.. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Mininni, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Marino, R.. Universite Lyon 2; FranciaFil: Pouquet, A.. State University of Colorado Boulder; Estados Unido

Finite dissipation and intermittency in magnetohydrodynamics

We present an analysis of data stemming from numerical simulations of decaying magnetohydrodynamic (MHD) turbulence up to grid resolution of 1536^3 points and up to Taylor Reynolds number of 1200. The initial conditions are such that the initial velocity and magnetic fields are helical and in equipartition, while their correlation is negligible. Analyzing the data at the peak of dissipation, we show that the dissipation in MHD seems to asymptote to a constant as the Reynolds number increases, thereby strengthening the possibility of fast reconnection events in the solar environment for very large Reynolds numbers. Furthermore, intermittency of MHD flows, as determined by the spectrum of anomalous exponents of structure functions of the velocity and the magnetic field, is stronger than for fluids, confirming earlier results; however, we also find that there is a measurable difference between the exponents of the velocity and those of the magnetic field, as observed recently in the solar wind. Finally, we discuss the spectral scaling laws that arise in this flow.Comment: 4 pages, 4 figure

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

We report results on rotating stratified turbulence in the absence of forcing, with large-scale isotropic initial conditions, using direct numerical simulations computed on grids of up to 4096^3 points. The Reynolds and Froude numbers are respectively equal to Re=5.4 x 10^4 and Fr=0.0242. The ratio of the Brunt-V\"ais\"al\"a to the inertial wave frequency, N/f, is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number R_B=ReFr^2=32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the large-scale dynamics, for which we find a spectrum compatible with the Bolgiano-Obukhov scaling, and confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation, and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow in the velocity and temperature fields, with local overturning events indicated by small Richardson numbers, and a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed.Comment: 19 pages, 9 figures (including compound figures

A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows

We explore some consequences of the ``alpha model,'' also called the ``Lagrangian-averaged'' model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid dynamics which filters velocity fields locally while leaving their associated vorticities unsmoothed, and has proved useful for high Reynolds number turbulence computations. We consider several known effects (selective decay, dynamic alignment, inverse cascades, and the probability distribution functions of fluctuating turbulent quantities) in magnetofluid turbulence and compare the results of numerical solutions of the primitive MHD equations with their alpha-model counterparts' performance for the same flows, in regimes where available resolution is adequate to explore both. The hope is to justify the use of the alpha model in regimes that lie outside currently available resolution, as will be the case in particular in three-dimensional geometry or for magnetic Prandtl numbers differing significantly from unity. We focus our investigation, using direct numerical simulations with a standard and fully parallelized pseudo-spectral method and periodic boundary conditions in two space dimensions, on the role that such a modeling of the small scales using the Lagrangian-averaged framework plays in the large-scale dynamics of MHD turbulence. Several flows are examined, and for all of them one can conclude that the statistical properties of the large-scale spectra are recovered, whereas small-scale detailed phase information (such as e.g. the location of structures) is lost.Comment: 22 pages, 20 figure

Rapid directional alignment of velocity and magnetic field in magnetohydrodynamic turbulence

We show that local directional alignment of the velocity and magnetic field fluctuations occurs rapidly in magnetohydrodynamics for a variety of parameters. This is observed both in direct numerical simulations and in solar wind data. The phenomenon is due to an alignment between the magnetic field and either pressure gradients or shear-associated kinetic energy gradients. A similar alignment, of velocity and vorticity, occurs in the Navier Stokes fluid case. This may be the most rapid and robust relaxation process in turbulent flows, and leads to a local weakening of the nonlinear terms in the small scale vorticity and current structures where alignment takes place.Comment: 4 pages, 6 figure

Stochastic Resonance in a simple model of magnetic reversals

We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification of stochastic resonance induced by turbulent fluctuations, i.e. the amplitude of the external periodic perturbation needed for stochastic resonance to occur is much smaller than the one estimated by the equilibrium probability distribution of the unperturbed system. We argue that similar amplifications can be observed in many physical systems where turbulent fluctuations are needed to maintain large scale equilibria.Comment: 6 page

Numerical solutions of the three-dimensional magnetohydrodynamic alpha-model

We present direct numerical simulations and alpha-model simulations of four familiar three-dimensional magnetohydrodynamic (MHD) turbulence effects: selective decay, dynamic alignment, inverse cascade of magnetic helicity, and the helical dynamo effect. The MHD alpha-model is shown to capture the long-wavelength spectra in all these problems, allowing for a significant reduction of computer time and memory at the same kinetic and magnetic Reynolds numbers. In the helical dynamo, not only does the alpha-model correctly reproduce the growth rate of magnetic energy during the kinematic regime, but it also captures the nonlinear saturation level and the late generation of a large scale magnetic field by the helical turbulence.Comment: 12 pages, 19 figure

Helicity cascades in rotating turbulence

The effect of helicity (velocity-vorticity correlations) is studied in direct numerical simulations of rotating turbulence down to Rossby numbers of 0.02. The results suggest that the presence of net helicity plays an important role in the dynamics of the flow. In particular, at small Rossby number, the energy cascades to large scales, as expected, but helicity then can dominate the cascade to small scales. A phenomenological interpretation in terms of a direct cascade of helicity slowed down by wave-eddy interactions leads to the prediction of new inertial indices for the small-scale energy and helicity spectra.Comment: 7 pages, 8 figure

Dynamo action at low magnetic Prandtl numbers: mean flow vs. fully turbulent motion

We compute numerically the threshold for dynamo action in Taylor-Green swirling flows. Kinematic calculations, for which the flow field is fixed to its time averaged profile, are compared to dynamical runs for which both the Navier-Stokes and the induction equations are jointly solved. The kinematic instability is found to have two branches, for all explored Reynolds numbers. The dynamical dynamo threshold follows these branches: at low Reynolds number it lies within the low branch while at high kinetic Reynolds number it is close to the high branch.Comment: 4 pages, 4 figure