  We study the magnetohydrodynamics of relativistic plasmas accounting for the
chiral magnetic effect (CME). To take into account the evolution of the plasma
velocity, obeying the Navier-Stokes equation, we approximate it by the Lorentz
force accompanied by the phenomenological drag time parameter. On the basis of
this ansatz, we obtain the contributions of both the turbulence effects,
resulting from the dynamo term, and the magnetic field instability, caused by
the CME, to the evolution of the magnetic field governed by the modified
Faraday equation. In this way, we explore the evolution of the magnetic field
energy and the magnetic helicity density spectra in the early Universe plasma.
We find that the right-left electron asymmetry is enhanced by the turbulent
plasma motion in a strong seed magnetic field compared to the pure the CME case
studied earlier for the hot Universe plasma in the same broken phase.
