Abstract

Direct numerical simulations of magnetohydrodynamic flows with regular grids of up to 1536³ points and at a unit magnetic Prandtl number allow for an investigation of the rate at which small scales develop. No forcing term is included and computations for both deterministic and random initial con... Show moreDirect numerical simulations of magnetohydrodynamic flows with regular grids of up to 1536³ points and at a unit magnetic Prandtl number allow for an investigation of the rate at which small scales develop. No forcing term is included and computations for both deterministic and random initial conditions are reported. Parallel current and vorticity sheets form at the same spatial locations, with a strong degree of correlation; these sheets further destabilize and fold or roll-up after an initial exponential growth phase. At high Reynolds numbers, a self-similar evolution of the current and vorticity maxima is found; these maxima grow as a cubic power of time within localized structures. The flow then reaches a finite dissipation rate independent of Reynolds number as was also found in MHD in two space dimensions. This evolution may be linked to the degree of nonlocality of nonlinear interactions in turbulent flows, to the amount of velocity-magnetic field correlation, and to the possibility of occurrence of non-universal behavior in MHD turbulence. Show less