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Home > About us > Media > Archived news > 2015 > Journal of Fluid Mechanics’ cover highlights LPP

Journal of Fluid Mechanics’ cover highlights LPP

Results by researchers at the LPP have recently been published showing some peculiar and novel properties of a special form of plasma turbulence known as weak wave magnetohydrodynamic turbulence. This type of turbulence which manifests itself in the presence of a very strong magnetic guide field, has until recently, only been studied via broad statistical calculations with some assumptions about the phase dynamics. With the help of massively parallel high resolution 3D direct numerical simulations, members of both “Magnetic Fusion” and “Space Plasma” teams at the LPP (Romain Meyrand, Khurom Kiyani and Sébastien Galtier) have been able to realise the intricate dynamics of this special system and show that not only do they verify the previous analytic calculations [Galtier et al., JPP, 2000], they also show similar phase dynamics of stronger fully developed turbulence via extreme bursty events, known aa ’intermittency’.

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The cover : one result of the simulations, a snapshot of the magnetic field modulus in a section perpendicular to the uniform magnetic field.

Crucially this intermittent behaviour, in turn due to the presence of coherent structures such as current sheets, is very intimately linked to the influence of a strongly nonlinear 2D condensate formed in the plane perpendicular due to slow and weak wave-wave interactions along the strong guide field. Their work has been recently published in the Journal of Fluid Mechanics (Rapids) [Meyrand et al., JFM, 2015] and a snapshot of their simulation adorns the cover of the journal.

One of the most striking features of strong hydrodynamic turbulence is the presence of both a complex chaotic spatial/temporal behavior and a remarkable degree of coherence. The small-scale correlations of turbulent motion are known to show significant deviations from Gaussian statistics usually expected in systems with a large number of degrees of freedom. This phenomenon, known as intermittency, has been the subject of much research and controversy since Batchelor and Townsend’s first experimental observation in 1949. It still challenges any tentative of rigorous analytical description from first principles (i.e. from the Navier- Stokes equations).
Recently, growing interest has been given to the study of intermittency in the weak wave turbulence (WWT) regime. Intermittency in WWT has been observed in the situation where coherent structures like sea foam or freak ocean waves are present. In these examples, intermittency is linked to the breakdown of the weak nonlinearity assumption induced by the WWT dynamics itself and therefore cannot be considered as an intrinsic property of this regime. In fact intermittency is at odds with classical WWT theory because of the random phase approximation which allows the asymptotic closure and resultant derivation of the WWT equations.
WWT magnetohydrodynamic (MHD) turbulence differs significantly from other cases because of the singular role played by the 2D modes. R. Meyrand, K. H. Kiyani and S. Galtier have shown that when the interactions with the 2D modes are artificially reduced the system exhibits an Iroshnikov-Kraichnan energy spectrum, whereas the expected exact solution is recovered with the full nonlinear system. In the latter case, strong intermittency has been found. This surprising result, has been explained by the influence of the 2D modes whose regime belongs to strong turbulence. A new log-Poisson law has been derived to describe intermittency in weak MHD turbulence which fits perfectly data from 3D direct numerical simulations and highlights the important role of current sheets parallel to the uniform magnetic field.
These results are important for the interpretation of space plasma turbulence observations and provides objective insights to the normally heated discussions on what constitutes turbulence in systems such as plasmas which host a rich variety of waves and instabilities and at the same time are inherently nonlinear. The results of this work confirm that the quintessential signature of turbulence in the form of intermittency is not simply a property of strong turbulence but it may also be found in a medium where WWT is present.

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Tutelles : CNRS Ecole Polytechnique Sorbonne Université Université Paris Sud Observatoire de Paris Convention : CEA
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