The magnetic Reynolds number R_M, is defined as the product of a
characteristic scale and associated flow speed divided by the microphysical
magnetic diffusivity. For laminar flows, R_M also approximates the ratio of
advective to dissipative terms in the total magnetic energy equation, but for
turbulent flows this latter ratio depends on the energy spectra and approaches
unity in a steady state. To generalize for flows of arbitrary spectra we define
an effective magnetic dissipation number, R_{M,e}, as the ratio of the
advection to microphysical dissipation terms in the total magnetic energy
equation, incorporating the full spectrum of scales, arbitrary magnetic Prandtl
numbers, and distinct pairs of inner and outer scales for magnetic and kinetic
spectra. As expected, for a substantial parameter range R_{M,e}\sim {O}(1) <<
R_M. We also distinguish R_{M,e} from {\tilde R}_{M,e} where the latter is an
effective magnetic Reynolds number for the mean magnetic field equation when a
turbulent diffusivity is explicitly imposed as a closure. That R_{M,e} and
{\tilde R}_{M,e} approach unity even if R_M>>1 highlights that, just as in
hydrodynamic turbulence,energy dissipation of large scale structures in
turbulent flows via a cascade can be much faster than the dissipation of large
scale structures in laminar flows. This illustrates that the rate of energy
dissipation by magnetic reconnection is much faster in turbulent flows, and
much less sensitive to microphysical reconnection rates compared to laminar
flows.Comment: 14 pages (including 2 figs), accepted by MNRA