Exact scaling laws for 3D electron MHD turbulence

A von Karman-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.