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

**F. Malara**^{1},
G. Nigro^{1}, P. Veltri^{1},
L. Sorriso-Valvo^{1}, V. Carbone^{1},
R. Marino^{1}, R. Bruno^{2},
A. Noullez^{3}

^{1}Dipartimento di
Fisica, Universita della Calabria, Rende, Italy

^{2}Istituto di Fisica dello Spazio
Interplanetario - INAF, Roma, Italy

^{3}Observatoire de la Cote d’ 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.