Magnetic helicity in magnetohydrodynamic turbulence with a mean magnetic field

A computational investigation of magnetic helicity of the fluctuating magnetic field Hm in ideal and freely decaying three-dimensional (3-D) magnetohydrodynamics (MHD) in the presence of a uniform mean magnetic field is performed. It is shown that for ideal 3-D MHD Hm, which is a rugged invariant in the absence of a mean magnetic field [Frisch et al., J. Fluid Mech. 77, 796 (1975)], decays from its initial value and proceeds to oscillate about zero. The decay of Hm is shown to result from the presence of a new ‘‘generalized’’ helicity invariant, which includes contributions from the uniform magnetic field. The loss of invariance of Hm will diminish the effects of inverse transfer of Hm on freely decaying turbulence. This is demonstrated in a discussion of the selective decay relaxation process.