Alain Noullez

Observation of Inertial Energy Cascade in Interplanetary Space Plasma

Direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), is observed in the solar wind by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yagloms law for MHD turbulence, a linear relation is indeed observed for the scaling of mixed third-order structure functions involving Elsässer variables. This experimental result firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.

Scaling laws of turbulence and heating of fast solar wind: the role of density fluctuations.

Incompressible and isotropic magnetohydrodynamic turbulence in plasmas can be described by an exact relation for the energy flux through the scales. This Yaglom-like scaling law has been recently observed in the solar wind above the solar poles observed by the Ulysses spacecraft, where the turbulence is in an Alfvénic state. An analogous phenomenological scaling law, suitably modified to take into account compressible fluctuations, is observed more frequently in the same data set. Large-scale density fluctuations, despite their low amplitude, thus play a crucial role in the basic scaling properties of turbulence. The turbulent cascade rate in the compressive case can, moreover, supply the energy dissipation needed to account for the local heating of the nonadiabatic solar wind.

Intermittent character of interplanetary magnetic field fluctuations

Interplanetary magnetic field magnitude fluctuations are notoriously more intermittent than velocity fluctuations in both fast and slow wind. This behavior has been interpreted in terms of the anomalous scaling observed in passive scalars in fully developed hydrodynamic turbulence. In this paper, the strong intermittent nature of the interplanetary magnetic field is briefly discussed comparing results performed during different phases of the solar cycle. The scaling properties of the interplanetary magnetic field magnitude show solar cycle variation that can be distinguished in the scaling exponents revealed by structure functions. The scaling exponents observed around the solar maximum coincide, within the errors, to those measured for passive scalars in hydrodynamic turbulence. However, it is also found that the values are not universal in the sense that the solar cycle variation may be reflected in dependence on the structure of the velocity field.

Analysis of cancellation in two-dimensional magnetohydrodynamic turbulence

A signed measure analysis of two-dimensional intermittent magnetohydrodynamic turbulence is presented. This kind of analysis is performed to characterize the scaling behavior of the sign-oscillating flow structures, and their geometrical properties. In particular, it is observed that cancellations between positive and negative contributions of the field inside structures are inhibited for scales smaller than the Taylor microscale, and stop near the dissipative scale. Moreover, from a simple geometrical argument, the relationship between the cancellation exponent and the typical fractal dimension of the structures in the flow is obtained.

Compressive turbulent cascade and heating in the solar wind

A turbulent energy cascade has been recently identified in high‐latitude solar wind data samples by using a Yaglom‐like relation. However, analogous scaling law, suitably modified to take into account compressible fluctuations, has been observed in a much more extended fraction of the same data set recorded by the Ulysses spacecraft. Thus, it seems that large scale density fluctuations, despite their low amplitude, play a major role in the basic scaling properties of turbulence. The compressive turbulent cascade, moreover, seems to be able to supply the energy needed to account for the local heating of the non‐adiabatic solar wind.

A model for two-dimensional bursty turbulence in magnetized plasmas

The nonlinear dynamics of two-dimensional electrostatic interchange modes in a magnetized plasma is investigated through a simple model that replaces the instability mechanism due to magnetic field curvature by an external source of vorticity and mass. Simulations in a cylindrical domain, with a spatially localized and randomized source at the center of the domain, reveal the eruption of mushroom-shaped bursts that propagate radially and are absorbed by the boundaries. Burst sizes and the interburst waiting times exhibit power-law statistics, which indicates long-range interburst correlations, similar to what has been found in sandpile models for avalanching systems. It is shown from the simulations that the dynamics can be characterized by a Yaglom relation for the third-order mixed moment involving the particle number density as a passive scalar and the E×B drift velocity, and hence that the burst phenomenology can be described within the framework of turbulence theory. Statistical features are qualitat...