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Solar wind fluctuations and the von Kármán–Howarth equations: The role of fourth-order correlations

The von Kármán-Howarth (vKH) hierarchy of equations relate the second-order correlations of the turbulent fluctuations to the third-order ones, the third-order to the fourth-order, and so on. We recently demonstrated [1] that for MHD, self-similar solutions to the vKH equations seem to require at least two independent similarity lengthscales (one for each Elsässer energy), so that compared to hydrodynamics a richer set of behaviors seems likely to ensue. Moreover, despite the well-known anisotropy of MHD turbulence with a mean magnetic field (B₀), the equation for the second-order correlation does not contain explicit dependence on B₀. We show that there is, however, implicit dependence on B₀ via the third-order correlations, which themselves have both explicit B₀-dependence and also their own implicit dependence through fourth-order correlations. Some subtleties and consequences of this implicit-explicit balance are summarized here. In addition, we present an analysis of simulation results showing that the evolution of turbulence can depend strongly on the initial fourth-order correlations of the system. This leads to considerable variation in the energy dissipation rates. Some associated consequences for MHD turbulence are discussed.
Journal Article
Type of thesis
Oughton, S., Wan. M., Matthaeus, W. H., & Servidio, S. (2013). Solar wind fluctuations and the von Kármán–Howarth equations: The role of fourth-order correlations. AIP Conference Proceedings, 1539, 251-254.
American Institute of Physics
Copyright © 2013 American Institute of Physics.