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Home > Research > Space Plasmas > Scientific topics > Turbulence


Turbulence is a universal phenomenon observed in fluids and plasmas. It is observed in a wide range of scales, from the vortices behind a bridge pier, to astrophysical scales. In plasmas, turbulence is characterized by disorganized behavior, swirling, chaotic, observed on all the characteristic quantities of the medium, the velocity but also the electromagnetic field.

  LPP team

G. Belmont, R. Grappin, S. Galtier, L. Rezeau, F. Sahraoui

 Selected publications

 Turbulence observations

To study turbulence, LPP space plasma team mainly use in situ magnetic field measurements made onboard spacecraft. The main regions of turbulence observation are the Solar Wind and magnetosheath (compressed solar wind region between the
bow shock) and the magnetopause. In the Earth vicinity, the measurements are made with CLUSTER and MMS. Measurements have also been performed around Saturn with Cassini. Fluxgate magnetometer give access to low frequencies (large scales); they are complemented at higher frequency by search coil measurements, generally designed and built at LPP.

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Magnetic fluctuations spectrum measured on board Cluster: In red measurements thanks to the FGM flux gate magnetometer and in blue the spectrum part measured with STAFF search coil magnetometer. The dotted line indicates the noise level of the STAFF instrument.

One observes wave spectra which present power laws (figure). This regular decreasing power behaviour is a characteristic of turbulent cascade: the energy is injected at large scale, then transmitted to smaller and smaller scales by means of vortices interaction. Signal processing work is being done at LPP for the precise analysis of turbulence: spectral analysis, filtering wave number (k-filtering) thanks to multi-satellite measurements, structure functions,....

Remote observations allow realizing that turbulence also exists in the stars or in the solar corona.

 Theoretical models

The interest is to understand the mechanisms of generation, transfer and dissipation of turbulence, from the large MHD scales toward scales smaller than those of the dynamics of ions, at which kinetic processes come into play. One of the theoretical difficulties is to take into account the collisionless aspect of the studied space plasma. In the case of the solar wind, the evolution of the turbulence depends on the characteristics of the medium, expanding from the Sun and highly magnetized. This magnetic field also introduces anisotropy which must be taken into account in the models.
There are two levels of turbulence: the strong turbulence and weak turbulence. In the first case, fluctuations in the plasma (e.g. magnetic field) are at least of the same order of magnitude as the mean magnetic field. In the second case, these variations are significantly smaller, which makes it possible to undertake perturbation expansions. Analytical and numerical studies are conducted at LPP on these two regimes (see Figure below).

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Strong and weak MHD turbulence. Direct MHD numerical simulation in strong magnetic field with a resolution of 3072x3072x256 points. This image shows, in a part of the plane transverse to the mean magnetic field, the intensity of the magnetic field fluctuations. The coexistence of strong and weak turbulence regimes is manifested by the presence of coherent structures (as large vortices) and smaller scale incoherent structures (Meyrand et al., 2015).

 Numerical models

The equations of plasma physics are complex since they must combine description of the plasma itself with the equations of the electromagnetic fields. Turbulence is inherently non-linear, the numerical simulation is a valuable tool, extensively developed at LPP.

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Expansion of a plasma volume from 0.2 to 1 AU : dynamics of the magnetic field (left) and the fluctuating velocity field (after subtracting the average radial field) (right). Initially (down), velocity and field lines are isotropic. At the end (top), after transverse stretching of the plasma volume by the radial wind, the magnetic field lines are mainly perpendicular to the radial direction (the mean radial direction is vertical) and the velocity lines are mainly radial, naturally forming micro-jets. These two combined evolutions are observed, and have important consequences for the turbulent cascade (Dong et al, 2014).

Regarding the turbulence several types of codes are used: Hall MHD, electron MHD, MHD 3D code or hybrid 2D with coordinates comoving with the solar wind expansion, MHD 2D code overall axisymmetric, Shell-model codes, Landau fluid.

CNRS Ecole Polytechnique Sorbonne Université Université Paris-Saclay Observatoire de Paris
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