Field theoretic calculation of energy cascade rates in nonhelical magnetohydrodynamic turbulence

Energy cascade rates and Kolmogorov's constant for nonhelical steady magnetohydrodynamic turbulence have been calculated by solving the flux equations to the first order in perturbation. For zero cross helicity and space dimension $d=3$, magnetic energy cascades from large length-scales to small length-scales (forward cascade). In addition, there are energy fluxes from large-scale magnetic field to small-scale velocity field, large-scale velocity field to small-scale magnetic field, and large-scale velocity field to large-scale magnetic field. Kolmogorov's constant for magnetohydrodynamics is approximately equal to that for fluid turbulence ($\approx 1.6$) for Alfv\'{e}n ratio $0.5 \le r_A \le \infty$. For higher space-dimensions, the energy fluxes are qualitatively similar, and Kolmogorov's constant varies as $d^{1/3}$. For the normalized cross helicity $\sigma_c \to 1$, the cascade rates are proportional to $(1-\sigma_c)/ (1+\sigma_c)$, and the Kolmogorov's constants vary significantly with $\sigma_c$.