On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence

We analyze the anisotropy of turbulence in an electrically conducting fluid in the presence of a uniform magnetic field, for low magnetic Reynolds number, using the quasistatic approximation. In the linear limit, the kinetic energy of velocity components normal to the magnetic field decays faster than the kinetic energy of component along the magnetic field [H. K. Moffatt, “On the suppression of turbulence by a uniform magnetic field,” J. Fluid Mech. 28, 571 (1967)]. However, numerous numerical studies predict a different behavior, wherein the final state is characterized by dominant horizontal energy. We investigate the corresponding nonlinear phenomenon using direct numerical simulations. The initial temporal evolution of the decaying flow indicates that the turbulence is very similar to the so-called two-and-a-half-dimensional flow [D. Montgomery and L. Turner, “Two-and-a-half-dimensional magnetohydrodynamic turbulence,” Phys. Fluids 25, 345 (1982)] and we offer an explanation for the dominance of horizontal kinetic energy.