Context : Turbulent diffusion of large-scale flows and magnetic fields play major roles in many astrophysical systems such as stellar convection zones and accretion disks .

Aims : Our goal is to compute turbulent viscosity and magnetic diffusivity , relevant for diffusing large-scale flows and magnetic fields , respectively , and their ratio , the turbulent magnetic Prandtl number , { Pm } _ { t } , for isotropically forced homogeneous turbulence .

Methods : We use simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow .
Turbulent viscosity is computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow .
Turbulent magnetic diffusivity is computed using the test-field method for a microphysical magnetic Prandtl number of unity .
The scale dependence of the coefficients is studied by varying the wavenumber of the imposed sinusoidal shear and test fields .

Results : We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude .
Furthermore , the turbulent viscosity depends on the fluid Reynolds number ( { Re } ) and scale separation ratio of turbulence .
The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian .
These results are similar to those obtained earlier for the turbulent magnetic diffusivity .
The results for the turbulent transport coefficients appear to converge at sufficiently high values of { Re } and the scale separation ratio .
However , a weak trend is found even at the largest values of { Re } , suggesting that the turbulence is not in the fully developed regime .
The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large { Re } whereas for small { Re } , we find values between 0.5 and 0.6 , although the data is insufficient to draw conclusions regarding asymptotics .

Conclusions : The turbulent magnetic diffusivity is in general consistently higher than the turbulent viscosity which is in qualitative agreement with analytic theories .
However , the actual value of { Pm } _ { t } found from the simulations ( \approx 0.9 \ldots 0.95 ) at large { Re } and scale separation ratio is higher than any of the analytic predictions that range between 0.4 and 0.8 .