Von Karman correlation similarity in solar wind magnetohydrodynamic turbulence

Abstract

A major development underlying hydrodynamic turbulence theory is the similarity decay hypothesis due to von Karman and Howarth, here extended empirically to plasma turbulence in the solar wind. In similarity decay the second-order correlation experiences a continuous transformation based on a universal functional form and a rescaling of energy and characteristic length. Solar wind turbulence follows many principles adapted from classical fluid turbulence, but previously this similarity property has not been examined explicitly. Here, we analyze an ensemble of Elsässer autocorrelation functions computed from Advanced Composition Explorer data at 1 astronomical unit (AU), and demonstrate explicitly that the two-point correlation functions undergo a collapse to a similarity form of the type anticipated from von Karman's hypothesis applied to weakly compressive magnetohydrodynamic turbulence. This provides a firm empirical basis for employing the similarity decay hypothesis to the Elsässer correlations that represent the incompressive turbulence cascade. This approach is of substantial utility in space turbulence data analysis, and for adopting von Karman-type heating rates in global and subgrid-scale dynamical modeling.