A phenomenology of isotropic magnetohydrodynamic turbulence subject to both rotation and applied magnetic field is presented .
It is assumed that the triple correlations decay-time is the shortest between the eddy turn-over time and the ones associated to the rotating frequency and Alfvén wave period .
For \mathrm { Pm } = 1 it leads to four kinds of piecewise spectra , depending on the four parameters , injection rate of energy , magnetic diffusivity , rotation rate and applied field .
With a shell model of MHD turbulence ( including rotation and applied magnetic field ) , spectra for \mathrm { Pm } \leq 1 are presented , together with the ratio between magnetic and viscous dissipation .
August 26 , 2020