Abstract
A von Kármán‐Howarth equation is derived for three‐dimensional (3D) electron magnetohydrodynamics (MHD) in the case of an homogeneous and isotropic turbulence. From this exact relation, we then derive the “one‐sixths” law for the third‐order correlation tensors; this is the analog of the Kolmogorov 4/5ths law for hydrodynamic turbulence. We show how this result is compatible with direct numerical simulations where a well‐extended k−7/3 energy spectrum is found. The observation of this exact relation in geophysical flows may be used as an evidence of the applicability of the electron MHD model.
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