Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of theenergy flux of the turbulent kinetic energy in the solar wind have been studied.Using present experimental technology in solar wind measurements we cannotdirectly measure the real volumetric dissipation rate, ε(t),but are constrained to represent it by its surrogate the energy flux near thedissipation range at the proton gyro scale. There is evidence for themultifractal nature of the so defined dissipation field ε(t),a result derived from the scaling exponents of its statistical moments. Thegeneralized dimension D_q has been determined and reveals thatthe dissipation field has a multifractal structure, which is not compatible witha scale-invariant cascade. The related multifractal spectrum αhas been estimated for the first time for MHD turbulence in the solar wind. Itsfeatures resemble those obtained for turbulent fluids and other nonlinearmultifractal systems. The generalized dimension D_q can forturbulence in high-speed streams be fitted well by the functional dependence ofthe p-model with a comparatively large parameter p₁=0.87,indicating a strongly intermittent multifractal energy cascade. The experimentalvalue for D_p/3 used in the scaling exponent s(p)of the velocity structure function gives an exponent that can describe some ofthe observations. The scaling exponent μ of the autocorrelationfunction of ε (t) has also been directly evaluated, being0.37. Finally, the mean dissipation rate was determined, which could be used insolar wind heating models