Turbulence, statistics and structures: an introduction

Pouquet, A.

doi:10.1007/bfb0102544

Cited by 15 publications

(20 citation statements)

References 156 publications

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“…Actually a lot of papers appeared in literature on computer simulations related to MHD turbulence. The interested reader can look at the book by Biskamp (1993) and the reviews by Pouquet (1993Pouquet ( , 1996. …”

Section: Numerical Simulationsmentioning

confidence: 99%

The Solar Wind as a Turbulence Laboratory

Bruno

Carbone

2013

Living Rev. Solar Phys.

974

957

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In this review we will focus on a topic of fundamental importance for both astrophysics and plasma physics, namely the occurrence of large-amplitude low-frequency fluctuations of the fields that describe the plasma state. This subject will be treated within the context of the expanding solar wind and the most meaningful advances in this research field will be reported emphasizing the results obtained in the past decade or so. As a matter of fact, Helios inner heliosphere and Ulysses' high latitude observations, recent multi-spacecrafts measurements in the solar wind (Cluster four satellites) and new numerical approaches to the problem, based on the dynamics of complex systems, brought new important insights which helped to better understand how turbulent fluctuations behave in the solar wind. In particular, numerical simulations within the realm of magnetohydrodynamic (MHD) turbulence theory unraveled what kind of physical mechanisms are at the basis of turbulence generation and energy transfer across the spectral domain of the fluctuations. In other words, the advances reached in these past years in the investigation of solar wind turbulence now offer a rather complete picture of the phenomenological aspect of the problem to be tentatively presented in a rather organic way.

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Section: Numerical Simulationsmentioning

confidence: 99%

The Solar Wind as a Turbulence Laboratory

Bruno

Carbone

2013

Living Rev. Solar Phys.

974

957

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“…For completeness, one can write the MHD equations in the incompressible case (see, e.g., Davidson, ; Galtier, ; Pouquet, , ), including the Hall current added to a (generalized) Ohm's law. The Hall MHD (HMHD) equations are

\frac{\partial boldv}{\partial t} = - boldv \cdot \nabla boldv - \nabla P + boldJ \times boldB + ν \nabla^{2} boldv - ν^{'} \nabla^{4} boldv,

\frac{\partial boldB}{\partial t} = \nabla \times ((), boldv \times boldB) - ϵ_{H} \nabla \times ((), boldJ \times boldB) + η \nabla^{2} boldB - η^{'} \nabla^{4} boldB,

together with ∇· v = 0,∇· B = 0.…”

Section: Coupling To a Magnetic Fieldmentioning

confidence: 99%

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Pouquet

Rosenberg

Stawarz

et al. 2019

Earth and Space Science

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We briefly review helicity dynamics, inverse and bidirectional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the nondissipative case, is transferred to small scales through nonlinear mode coupling. Fifty years ago, it was realized that, for a two‐dimensional fluid, energy cascades instead to larger scales and so does magnetic excitation in MHD. However, evidence obtained recently indicates that, in fact, for a range of governing parameters, there are systems for which their ideal invariants can be transferred, with constant fluxes, to both the large scales and the small scales, as for MHD or rotating stratified flows, in the latter case including quasi‐geostrophic forcing. Such bidirectional, split, cascades directly affect the rate at which mixing and dissipation occur in these flows in which nonlinear eddies interact with fast waves with anisotropic dispersion laws, due, for example, to imposed rotation, stratification, or uniform magnetic fields. The directions of cascades can be obtained in some cases through the use of phenomenological arguments, one of which we derive here following classical lines in the case of the inverse magnetic helicity cascade in electron MHD. With more highly resolved data sets stemming from large laboratory experiments, high‐performance computing, and in situ satellite observations, machine learning tools are bringing novel perspectives to turbulence research. Such algorithms help devise new explicit subgrid‐scale parameterizations, which in turn may lead to enhanced physical insight, including in the future in the case of these new bidirectional cascades.

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“…With ν = 0, η = 0, the energy E = v 2 + b 2 /2 and cross helicity H C = v · b /2, are conserved [15], with the magnetic helicity H M = A · b in 3D. Defining D ± /Dt = ∂ t + z ± · ∇, one can symmetrize Eqs.(1) and obtain [11]: …”

mentioning

confidence: 99%

“…[11]), because of the large-scale gradients of the velocity and magnetic fields, assumed given, stretching the vorticity and current. The phase beyond the linear stage, though, is still unclear.…”

mentioning

confidence: 99%

Small-Scale Structures in Three-Dimensional Magnetohydrodynamic Turbulence

2006

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We investigate using direct numerical simulations with grids up to 1536 3 points, the rate at which small scales develop in a decaying three-dimensional MHD flow both for deterministic and random initial conditions. Parallel current and vorticity sheets form at the same spatial locations, and further destabilize and fold or roll-up after an initial exponential phase. At high Reynolds numbers, a self-similar evolution of the current and vorticity maxima is found, in which they grow as a cubic power of time; the flow then reaches a finite dissipation rate independent of Reynolds number.Magnetic fields are ubiquitous in the cosmos and play an important dynamical role, as in the solar wind, stars or the interstellar medium. Such flows have large Reynolds numbers and thus nonlinear mode coupling leads to the formation of strong intermittent structures. It has been observed that such extreme events in magnetohydrodynamics (MHD) are more intense than for fluids; for example, wings of Probability Distribution Functions of field gradients are wider and one observes a stronger departure from purely self-similar linear scaling with the order of the anomalous exponents of structure functions [1]. Since Reynolds numbers are high but finite, viscosity and magnetic resistivity play a role, tearing mode instabilities develop and reconnection takes place. The question then becomes at what rate does dissipation occur, as the Reynolds number increases? What is the origin of these structures, and how fast are they formed? This is a long-standing problem in astrophysics, e.g. in the context of reconnection events in the magnetopause, or of heating of solar and stellar corona. In such fluids, many other phenomena may have to be taken into account, such as finite compressibility and ionization, leading to a more complex Ohm's law with e.g. a Hall current or radiative or gravitational processes to name a few. Many aspects of the two-dimensional (2D) case are understood, but the three-dimensional (3D) turbulent case remains more obscure. Pioneering works [2] show that the topology of the reconnecting region, more complex than in 2D, can lead to varied behavior.The criterion for discriminating between a singular and a regular behavior in the absence of magnetic fields follows the seminal work by Beale, Kato and Majda (hereafter BKM) [3] where, for a singularity to develop in the Euler case, the time integral of the supremum of the vorticity must grow as (t−t * ) −α with α ≥ 1 and t * the singularity time. In MHD [4], one deals with the Elsässer fields z ± = v±b and ω ± = ω±j = ∇×(v±b), with ω the vorticity, v the velocity, j the current density and b = ∇×A the induction in dimensionless Alfvenic units, A being the vector potential. Intense current sheets are known to form at either magnetic nulls (b ≡ 0) or when one or two (but not all) components of the magnetic field go to zero or have strong gradients. In two dimensional configurations, a vortex quadrupole is also associated with these structures. The occurrence of singularities in MH...

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Turbulence, statistics and structures: an introduction

Cited by 15 publications

References 156 publications

The Solar Wind as a Turbulence Laboratory

The Solar Wind as a Turbulence Laboratory

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Small-Scale Structures in Three-Dimensional Magnetohydrodynamic Turbulence

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