Residual energy in magnetohydrodynamic turbulence and in the solar wind

Recent observations indicate that kinetic and magnetic energies are not in equipartition in the solar wind turbulence. Rather, magnetic fluctuations are more energetic and have somewhat steeper energy spectrum compared to the velocity fluctuations. This leads to the presence of the so-called residual energy E_r=E_v-E_b in the inertial interval of turbulence. This puzzling effect is addressed in the present paper in the framework of weak turbulence theory. Using a simple model of weakly colliding Alfv\'en waves, we demonstrate that the kinetic-magnetic equipartition indeed gets broken as a result of nonlinear interaction of Alfv\'en waves. We establish that magnetic energy is indeed generated more efficiently as a result of these interactions, which proposes an explanation for the solar wind observations.