Energy Balance and Cascade in MHD Turbulence in the Solar Corona and in the Solar Wind

F. Malara1, G. Nigro1, P. Veltri1, L. Sorriso-Valvo1, V. Carbone1, R. Marino1, R. Bruno2, A. Noullez3

1Dipartimento di Fisica, Universita della Calabria, Rende, Italy
2Istituto di Fisica dello Spazio Interplanetario - INAF, Roma, Italy
3Observatoire de la Cote dí Azur, Nice, France

We discuss two aspects of turbulence in the heliospace. The first concernes turbulence in closed magnetic structures in the corona. The dynamics of fluctuations in a closed coronal structure is regulated by two phenomena: the resonance excited by motions at the loop basis, that stores energy within the loop; nonlinear couplings, that move energy towards smaller scales. The energy balance is evaluated using both an analytical and a numerical approach, the latter using the so-called hybrid shell model. A scaling law is derived for the input energy flux, that turns out to be independent of nonlinear couplings and is determined by slow (DC) fluctuations. The nonlinear flux is due to interactions between eigenmodes at different perpendicular wavelengths, but with the same parallel wavelength. The energy balance allows for an estimation of velocity fluctations that in agreement with measures of nonthermal velocity in the solar corona. The fluctuation spectrum is formed by an injection range at large scales, a pre-inertial range where magnetic energy dominates kinetic energy, an inertial range where the turbulence behaves as in an unbounded system, and a dissipative range. The second issue concernes the properties of solar wind turbulence. Incompressible and isotropic MHD turbulence can be described by an exact relation for the energy flux through the scales, that has been observed by the Ulysses spacecraft in the high-latitude solar wind. An analogous scaling law, suitably modified to take into account compressible fluctuations, can be observed in a more extended fraction of the same dataset. Large scale density fluctuations, despite their low amplitude, play thus a crucial role in the basic scaling properties of turbulence.