Inverse cascade of kinetic energy in two-dimensional β-Plane magnetohydrodynamic turbulence

2020 ◽  
Author(s):  
Timofey Zinyakov ◽  
Arakel Petrosyan
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Cascade Process ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Self Similarity ◽  
Magnetohydrodynamic Turbulence ◽  
Zonal Flows ◽  
Inverse Cascade ◽  
Kolmogorov Spectrum

<p>Numerical studies of two-dimensional β-plane homogeneous magnetohydrodynamic turbulence are presented. The study of the fundamental properties of such turbulence allows understanding the evolution of various astrophysical objects from the Sun and stars to planetary systems, galaxies, and galaxy clusters. Energy spectra and cascade process in two-dimensional β-plane MHD are studied.</p><p>In this work the equations of two-dimensional magnetohydrodynamics with the Coriolis force in the β-plane approximation are used for the qualitative analysis and numerical simulation of processes in plasma astrophysics. The equations are solved on a square box of edge size 2π with periodic boundary conditions applying a the pseudospectral method using the 2/3 rule for dealiasing. The results of numerical simulation of two-dimensional β-plane MHD turbulence with a spatial resolution of 1024 × 1024 and 4096 × 4096 with different Rossby parameters β and different Reynolds numbers are presented.</p><p>It is found that only unsteady zonal flows with complex temporal dynamics are formed in two-dimensional β-plane magnetohydrodynamic turbulence. It is shown that flow nonstationarity is due to the appearance of isotropic magnetic islands caused by the Lorentz force in the system. The formation of Iroshnikov–Kraichnan spectrum is shown in the early stages of evolution of two-dimensional β-plane magnetohydrodynamic turbulence. The self-similarity of the decay of Iroshnikov–Kraichnan spectrum is studied. On long time scale violation of self-similarity of the decay and formation of Kolmogorov spectrum is discovered. The inverse cascade of kinetic energy, which is characteristic of the detected Kolmogorov spectrum, provides the formation of zonal flows.</p><p>This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).</p>

scholarly journals Numerical simulation of reynolds number effect of a free incompressible isothermal turbulent coaxial jet

2022 ◽  
pp. 3-11
Author(s):  
Olanrewaju Miracle Oyewola ◽  
Olawale Saheed Ismail ◽  
Lateef Anjola Sanni
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Finite Volume ◽  
Radial Profile ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Self Similarity ◽  
Potential Core

This paper studies the effect of Reynolds number on a two-dimensional free incompressible isothermal coaxial turbulent jet over a range of high Reynolds numbers. This is necessary because of its application in noise control and mixing. The Reynolds numbers at the nozzle exit were 9824, 19648, 29472, 39296 and 49120. The models were designed in ANSYS Design Modeler and the numerical simulation was done using a finite volume based Computational Fluid Dynamics (CFD) in ANSYS FLUENT using the two-dimensional Realizable turbulence model. The Governing equations were discretized using the finite volume method with the solution based on the PISO algorithm. The decay of centerline velocity, turbulent kinetic energy profile, the radial profile of axial velocity and similarity profile were investigated along the flow direction. Contour plot indicates that the velocity is high at the jet exit and decreases downstream due to the rapid mixing of the inner and outer jet and the surrounding fluid. It is found generally that Reynolds number plays significant role especially before self-similarity region. The result shows that increasing the Reynolds number give rise to more turbulence which in turn decreases the potential core length, turbulent kinetic energy and enhances the mixing of the fluid. However, at the jet exit, the flow with the lowest Reynolds number has the highest turbulent kinetic energy because it suffers the greater shear. The spreading of the jet was more or less independent of the Reynolds number beyond the self-similarity region. It is also found that the velocity profile is brought to congruence at about z/D=25 for the Reynolds numbers considered

scholarly journals On energetics and inertial-range scaling laws of two-dimensional magnetohydrodynamic turbulence

2012 ◽  
Vol 703 ◽  
pp. 238-254 ◽  
Author(s):  
Luke A. K. Blackbourn ◽  
Chuong V. Tran
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Energy Flux ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Inertial Range ◽  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Direct Energy ◽  
Energy Equipartition

AbstractWe study two-dimensional magnetohydrodynamic turbulence, with an emphasis on its energetics and inertial-range scaling laws. A detailed spectral analysis shows that dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralizes the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. This result is consistent with a qualitative prediction of energy transfer reduction due to Alfvén wave effects by the Iroshnikov–Kraichnan theory (which was originally formulated for magnetohydrodynamic turbulence in three dimensions). We numerically confirm the correlation between dynamo action and direct magnetic energy flux and investigate the applicability of quantitative aspects of the Iroshnikov–Kraichnan theory to the present case, particularly its predictions of energy equipartition and ${k}^{\ensuremath{-} 3/ 2} $ spectra in the energy inertial range. It is found that for turbulence satisfying the Kraichnan condition of magnetic energy at large scales exceeding total energy in the inertial range, the kinetic energy spectrum, which is significantly shallower than ${k}^{\ensuremath{-} 3/ 2} $, is shallower than its magnetic counterpart. This result suggests no energy equipartition. The total energy spectrum appears to depend on the energy composition of the turbulence but is clearly shallower than ${k}^{\ensuremath{-} 3/ 2} $ for $r\approx 2$, even at moderate resolutions. Here $r\approx 2$ is the magnetic-to-kinetic energy ratio during the stage when the turbulence can be considered fully developed. The implication of the present findings is discussed in conjunction with further numerical results on the dependence of the energy dissipation rate on resolution.

Small-scale structure of two-dimensional magnetohydrodynamic turbulence

1979 ◽  
Vol 90 (1) ◽  
pp. 129-143 ◽  
Author(s):  
Steven A. Orszag ◽  
Cha-Mei Tang
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Three Dimensional ◽  
Scale Structure ◽  
Magnetohydrodynamic Flow ◽  
Small Scale ◽  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Hydrodynamic Turbulence ◽  
Small Scale Structure

The formation of singularities in two-dimensional magnetohydrodynamic flow is investigated by direct numerical simulation. It is shown that two-dimensional magnetohydrodynamic turbulence is not as singular as three-dimensional hydrodynamic turbulence (in the sense that it has a less highly excited small-scale structure) but that it is more singular than two-dimensional hydrodynamic turbulence.

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

2008 ◽  
Vol 86 (10) ◽  
pp. 1203-1207
Author(s):  
M Momeni ◽  
M Moslehi-Fard
Keyword(s):  
Three Dimensional ◽  
Qualitative Change ◽  
Mhd Turbulence ◽  
Self Similarity ◽  
Simulation Data ◽  
Magnetohydrodynamic Turbulence ◽  
Exponential Tails ◽  
Turbulent Field ◽  
Field Fluctuations ◽  
52.35 Ra

High-resolution direct numerical simulation data for three-dimensional magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box are used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. The energy PDFs exhibit similarity over all scales of the turbulent system since they show no substantial qualitative change in shape as the scale of the fluctuations varies. This is in sharp and surprising contrast to the well-known behavior of PDFs of turbulent field fluctuations of, for example, velocity, and magnetic and Elsässer fields. The PDFs have exponential tails and satisfy the function P(| δX |) ~ exp(–A | δX | μ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the scale of length varies. The compensated structure functions exhibit self-similarity for the respective fluctuations, and it is a reliable way in turbulence. PACS Nos.: 52.30.–q , 52.30.Cv , 52.35.Ra , 52.65.–y

scholarly journals Anisotropy in MHD turbulence due to a mean magnetic field

1983 ◽  
Vol 29 (3) ◽  
pp. 525-547 ◽  
Author(s):  
John V. Shebalin ◽  
William H. Matthaeus ◽  
David Montgomery
Keyword(s):  
Magnetic Field ◽  
Reynolds Numbers ◽  
Combined Effects ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
High Wavenumbers

The development of anisotropy in an initially isotropie spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops through the combined effects of an externally imposed d.c. magnetic field and viscous and resistive dissipation at high wavenumbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wavenumbers.

Direct numerical simulation of forced MHD turbulence at low magnetic Reynolds number

1998 ◽  
Vol 358 ◽  
pp. 299-333 ◽  
Author(s):  
OLEG ZIKANOV ◽  
ANDRE THESS
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Boundary Conditions ◽  
Interaction Parameter ◽  
Three Dimensional ◽  
Magnetic Interaction ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetic Interaction Parameter

The transformation of initially isotropic turbulent flow of electrically conducting incompressible viscous fluid under the influence of an imposed homogeneous magnetic field is investigated using direct numerical simulation. Under the assumption of large kinetic and small magnetic Reynolds numbers (magnetic Prandtl number Pm[Lt ]1) the quasi-static approximation is applied for the computation of the magnetic field fluctuations. The flow is assumed to be homogeneous and contained in a three-dimensional cubic box with periodic boundary conditions. Large-scale forcing is applied to maintain a statistically steady level of the flow energy. It is found that the pathway traversed by the flow transformation depends decisively on the magnetic interaction parameter (Stuart number). If the magnetic interaction number is small the flow remains three-dimensional and turbulent and no detectable deviation from isotropy is observed. In the case of a strong magnetic field (large magnetic interaction parameter) a rapid transformation to a purely two-dimensional steady state is obtained in agreement with earlier analytical and numerical results for decaying MHD turbulence. At intermediate values of the magnetic interaction parameter the system exhibits intermittent behaviour, characterized by organized quasi-two-dimensional evolution lasting several eddy-turnover times, which is interrupted by strong three-dimensional turbulent bursts. This result implies that the conventional picture of steady angular energy transfer in MHD turbulence must be refined. The spatial structure of the steady two-dimensional final flow obtained in the case of large magnetic interaction parameter is examined. It is found that due to the type of forcing and boundary conditions applied, this state always occurs in the form of a square periodic lattice of alternating vortices occupying the largest possible scale. The stability of this flow to three-dimensional perturbations is analysed using the energy stability method.

scholarly journals On uniqueness of transfer rates in magnetohydrodynamic turbulence

2019 ◽  
Vol 85 (5) ◽  
Author(s):  
Franck Plunian ◽  
Rodion Stepanov ◽  
Mahendra Kumar Verma
Keyword(s):  
Kinetic Energy ◽  
Transfer Rate ◽  
Stokes Equations ◽  
Magnetic Energy ◽  
A Priori ◽  
Magnetic Helicity ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
Transfer Rates ◽  
Induction Equation

In hydrodynamic and MHD (magnetohydrodynamic) turbulence, formal expressions for the transfer rates rely on integrals over wavenumber triads $(\boldsymbol{k},\boldsymbol{p},\boldsymbol{q})$ satisfying $\boldsymbol{k}+\boldsymbol{p}+\boldsymbol{q}=0$ . As an example $S_{E}^{uu}(\boldsymbol{k}\mid \boldsymbol{p},\boldsymbol{q})$ denotes the kinetic energy transfer rate to the mode $\boldsymbol{k}$ , from the two other modes in the triad, $\boldsymbol{p}$ and $\boldsymbol{q}$ . However as noted by Kraichnan (Phys. Rev., vol. 111, 1958, pp. 1747–1747), in $S_{E}^{uu}(\boldsymbol{k}\mid \boldsymbol{p},\boldsymbol{q})$ , what fraction of the energy transferred to the mode $\boldsymbol{k}$ originated from $\boldsymbol{p}$ and which from $\boldsymbol{q}$ is unknown. Such an expression is thus incongruent with the customary description of turbulence in terms of two-scale energy exchange. Notwithstanding this issue, Dar et al. (Physica D, vol. 157 (3), 2001, pp. 207–225) further decomposed these transfers into separate contributions from $\boldsymbol{p}$ -to- $\boldsymbol{k}$ and $\boldsymbol{q}$ -to- $\boldsymbol{k}$ , thus introducing the concept of mode-to-mode transfers that they applied to MHD turbulence. Doing so, they had to set aside additional transfers circulating within each triad, but failed to calculate them. In the present paper we explain how to derive the complete expressions of the mode-to-mode transfers, including the circulating transfers. We do it for kinetic energy and kinetic helicity in hydrodynamic turbulence, for kinetic energy, magnetic energy and magnetic helicity in MHD turbulence. We find that the degree of non-uniqueness of the energy transfers derived from the induction equation is a priori higher than the one derived from the Navier–Stokes equations. However, separating the contribution of magnetic advection from magnetic stretching, the energy mode-to-mode transfer rates involving the magnetic field become uniquely defined, in striking contrast to the hydrodynamic case. The magnetic helicity mode-to-mode transfer rate is also found to be uniquely defined, contrary to kinetic helicity in hydrodynamics. We find that shell-to-shell transfer rates have the same properties as mode-to-mode transfer rates. Finally calculating the fluxes, we show how the circulating transfers cancel in accordance with conservation laws.

scholarly journals The influence of a mean magnetic field on three-dimensional magnetohydrodynamic turbulence

1994 ◽  
Vol 280 ◽  
pp. 95-117 ◽  
Author(s):  
Sean Oughton ◽  
Eric R. Priest ◽  
William H. Matthaeus
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
Incompressible Mhd

Building on results from two-dimensional magnetohydrodynamic (MHD) turbulence (Shebalin, Matthaeus & Montgomery 1983), the development of anisotropic states from initially isotropic ones is investigated numerically for fully three-dimensional incompressible MHD turbulence. It is found that when an external d.c. magnetic field (B0) is imposed on viscous and resistive MHD systems, excitations are preferentially transferred to modes with wavevectors perpendicular to B0). The anisotropy increases with increasing mechanical and magnetic Reynolds numbers, and also with increasing wavenumber. The tendency of B0 to inhibit development of turbulence is also examined.

Sign in / Sign up

Export Citation Format

Share Document