von Karman Correlation Similarity of the Turbulent Interplanetary Magnetic Field

Abstract

A major development underlying much of hydrodynamic turbulence theory is the similarity decay hypothesis due to von Karman and Howarth here extended empirically to magnetic field fluctuations 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 magnetic correlation functions computed from Advanced Composition Explorer data at 1 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. This provides for the first time a firm empirical basis for employing the similarity decay hypothesis to the magnetic field, one of the primitive variables of magnetohydrodynamics, and one frequently more accessible from spacecraft instruments. 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.