Turbulent drag reduction in magnetohydrodynamic and quasi-static magnetohydrodynamic turbulence

In hydrodynamic turbulence, the kinetic energy injected at large scales cascades to the inertial range, leading to a constant kinetic energy flux. In contrast, in magnetohydrodynamic (MHD) turbulence, a fraction of kinetic energy is transferred to the magnetic energy. Consequently, for the same kinetic energy injection rate, the kinetic energy flux in MHD turbulence is reduced compared to its hydrodynamic counterpart. This leads to relative weakening of the nonlinear term ($\la | ({\bf u}\cdot \nabla) {\bf u} | \ra$, where ${\bf u}$ is the velocity field) and turbulent drag, but strengthening of the velocity field in MHD turbulence. We verify the above using shell model simulations of hydrodynamic and MHD turbulence. Quasi-static MHD turbulence too exhibits turbulent drag reduction similar to MHD turbulence.