The third-order law for increments in magnetohydrodynamic turbulence with constant shear

We extend the theory for third-order structure functions in homogeneous incompressible magnetohydrodynamic turbulence to the case in which a constant velocity shear is present. A generalization is found of the usual relation [Politano and Pouquet, Phys. Rev. E 57, 21 (1998)] between third-order structure functions and the dissipation rate in steady inertial range turbulence, in which the shear plays a crucial role. In particular, the presence of shear leads to a third-order law which is not simply proportional to the relative separation. Possible implications for laboratory and space plasmas are discussed. (C) 2009 American Institute of Physics. [doi:10.1063/1.3240333]