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

摘要

We extend the theory for third-order structure functions in homogeneous incompressiblemagnetohydrodynamic turbulence to the case in which a constant velocity shear is present. Ageneralization 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 lawwhich is not simply proportional to the relative separation. Possible implications for laboratory andspace plasmas are discussed.