Measuring and understanding space turbulence

International audienceFor many physical issues including reconnection, the role of waves and turbulence is likely to be predominant in space physics. This role can be viewed as a natural consequence of the general properties of turbulence, but these properties, although widely recognized in hydrodynamics, are much less familiar in plasmas. The connections between the different media, neutral or ionized, are presented first, in order to set up the décor and introduce what has been done recently to improve our knowledge about this topic and what can be done in the future. For the experimental point of view, the main emphasis is put on the new results brought by the Cluster mission: when variations are observed from mono-spacecraft measurements, it is impossible to determine to what extent they are due to intrinsic temporal variations or to crossing of spatial gradients, and in the second case, what are the size, the velocity, and the 3-D shape of the gradient sheets. The Cluster mission, with its four spacecraft, has been designed to disentangle as much as possible this spatio-temporal ambiguity, which is actually mandatory for characterizing the space turbulence, especially whenever the spectrum involves an unknown Doppler effect and when it cannot be assumed to be isotropic. Taking the example of the plasma turbulence in the terrestrial magnetosheath, we show how the k-filtering technique constitutes the appropriate tool to make the best use of the 4-point measurements for this objective. For the theoretical point of view, the main emphasis is put on the “weak turbulence” conditions, which seem to be frequently met, and which allow developing the theory beyond the usual heuristic and dimensional approaches. Because of the natural complexity of the calculations implied by this approach, it has not been possible to apply it up to now beyond the simple frame of incompressible ideal MHD, which proves to be quite insufficient for interpreting the observations. We show how recent results, using the Hamiltonian formalism of continuous media, constitute the first important step for overcoming these difficulties