The solar-wind magnetohydrodynamic turbulence is observed to be mainly made of Alfvenic fluctuations propagating away from the sun. It is shown that such an asymmetric state is a general consequence of the evolution of developed magnetohydrodynamic turbulence, which, starting from an initial asymmetry between modes with cross helicity +1 and -1, tends, as a consequence of nonlinear interactions, towards a state where the only modes left are those initially prevailing (with either cross helicity +1 or -1).PACS numbers: 96.50.Dj, 96.60.Vg Theoretical investigations of strong hydromagnetic turbulence have always dealt so far with the isotropic case" and most often with the case where the average magnetic field is zero. '4 In the latter case, Kraichnan' has derived, using dimensional arguments, a 0 ' ' power law for the spectrum of the magnetic and kinetic energy densities of the fluctuations in the stationary state. The difference in the spectral index with respect to that of the Kolmogorov spectrum of isotropic hydrodynamic turbulence is due to the presence, in the smaller scales, of Alfvdn waves propagating in the magnetic field of the larger-scale eddies, thus impeding the energy transfer in this range of high wave numbers.Observations of incompressible magnetohydrodynamic (MHD) turbulence in the magnetized plasma of interplanetary space' ' indicate, however, ' that the existence of these Alfvd'n waves is not the only peculiar feature of MHD with respect to hydrodynamic turbulence.On the one hand, the spectral energy density of magnetic fluctuations E(k) defined by (5B')/4vp= f F(k) dk(1) (p being the plasma mass density) seems to follow a power law E(k)~k " with a spectral index v ranging from 1.2 to 2, for frequencies between 10 ' and 10 Hz. Although the scatter of the observed values of v precludes a definite identification with either a Kolmogorov or a Kraichnan spectrum, the observed power law is expected to result from a nonlinear energy cascade. 5v = + &B/(4 tt p) (2) the sign depending on the polarity of the average magnetic field and being such that only Alfvdnic fluctuations propagating away from the sun are observed. Notice that, in terms of the so-called cross helicity of hydromagnetic turbulence, " the observational result (2) implies that the MHD turbulence in the solar wind is either in a state characterized by the value +1 for the cross helicity, or in a -1 state.It is a simple matter to show that, if condition (2) is satisfied, there are no longer nonlinear interactions which is in apparent contrast with the presence of a spectrum. To see this, we write the equations for incompressible MHD fluctuations as" where 1 ( B ) (4) and C"=(B)/(4zp)~' is the Alfvenic speed in the average field (B). The above equations refer to Qn the other hand, in the same domain of wave vectors, and mainly in the trailing edges of fast solar-wind streams, one observes a striking correlation between the velocity 5v and magnetic fluctuations 6B which satisfy to a good degree the relation 144
