Abstract
<p>Turbulence in the solar wind is developed along a vast range of scales, generally under weakly compressible and strong magnetic field plasma conditions. <br>The effects of weakly and moderate compressibility (Mach ≤1) and turbulence anisotropy on the energy transfer rate are investigated at MHD and Hall MHD scales. For this purpose, the results of two and three-dimensional compressible Hall MHD simulations are analyzed using a new form of the Karman-Howarth-Monin (KHM) equations that accounts for compressible effects down to Hall MHD scales.<br>The KHM are dynamic equations directly derived from the basic fluid equations that describe the plasma, such as the Hall MHD equations. They provide a relation between the two-point cross-correlations in real space or II-order structure functions, the III-order structure functions and the energy cascade rate of turbulence. These relations depend upon turbulence anisotropy. The effects of compressibility and the Hall term on anisotropy and the estimation of the energy cascade rate via the KHM equations are discussed.</p>
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