Abstract: The direct numerical simulation based on the current density conservative scheme was employed to calculate the turbulent Taylor-Couette flow of an electrically conducting fluid in an axial magnetic field. The generation of negative velocity due to the interaction of magnetic field with induced current， and the effect of magnetic field on the mean flow field were revealed， when two cylinders had the same potentials. By using two kinds of averaged method， the total fluctuations in the flow field were divided into two parts，i.e.， the contribution of mean Taylor vortex flow and the contribution of turbulence. Consequently， several cases were calculated to investigate the effect of magnetic field on the contribution， and comparation the effects of axial magnetic field on from mean Taylor vortex flow and the turbulent flow.

Key words: Taylor vortex flow, Taylor-Couette flow, turbulence, magnetic field, direct numerical simulation