The third-order law for magnetohydrodynamic turbulence with constant shear

The scaling laws of mixed third‐order structure functions for isotropic, homogeneous, and incompressible magnetohydrodynamic (MHD) turbulence have been recently applied in solar wind studies, even though there is recognition that isotropy is not well satisfied. Other studies have taken account of the anisotropy induced by a constant mean magnetic field. However, large‐scale shear can also cause departures from isotropy. Here we examine shear effects in the simplest case, and derive the third‐order laws for MHD turbulence with constant shear, where homogeneity is still assumed. This generalized scaling law has been checked by data from direct numerical simulations (DNS) of two‐dimensional (2D) MHD and is found to hold across the inertial range. These results suggest that third‐order structure function analysis and interpretation in the solar wind should be undertaken with some caution, since, when present, shear can change the meaning of the third‐order relations