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Residual Energy in Magnetohydrodynamic Turbulence

There is mounting evidence in solar wind observations and in numerical simulations that kinetic and magnetic energies are not in equipartition in magnetohydrodynamic turbulence. The origin of their mismatch, the residual energy E_r=E_v-E_b, is not well understood. In the present work this effect is studied analytically in the regime of weak magnetohydrodynamic turbulence. We find that residual energy is spontaneously generated by turbulent dynamics, and it has a negative sign, in good agreement with the observations. We obtain that the residual energy condenses around k_||=0 with its k_||-spectrum broadening linearly with k_perp, where k_|| and k_perp are the wavenumbers parallel and perpendicular to the background magnetic field, and the field-perpendicular spectrum of the residual energy has the scaling E_r(k_perp)\propto k_perp^{-1} in the inertial interval. These results are found to be in agreement with numerical simulations. We propose that residual energy plays a fundamental role in Alfvenic turbulence and it should be taken into account for correct interpretation of observational and numerical data.