  In order to gain deeper insight into the physics of the novel rotating
solution of nonideal transverse magnetohydrodynamics (MHD), presented in one of
our recent works, we replace the previously considered Maxwell theory with the
${\cal{CP}}$ violating Maxwell-Chern-Simons (MCS) theory. In this way,
dissipationless chiral magnetic (CM) and anomalous Hall (AH) currents appear in
the MCS equation of motion, that, together with equations of relativistic
hydrodynamics, builds the set of constitutive equations of the nonideal
transverse Chern-Simons magnetohydrodynamics (CSMHD). We are, in particular,
interested in the effect of these currents on the evolution of electromagnetic
fields in a uniformly and longitudinally expanding quark-gluon plasma with
chirality imbalance. Combining the constitutive equations of CSMHD under these
assumptions, we arrive, as expected, at two distinct rotating and nonrotating
solutions for electromagnetic fields. The rotation occurs with increasing
rapidity and a constant angular velocity $\omega_{0}$. Remarkably, the relative
angle between the electric and magnetic fields, $\delta$, turns out to be given
by the coefficient of AH current $\kappa_{E}$ and the electric conductivity of
the medium $\sigma$, as $\delta=\tan^{-1}(\kappa_{E}/\sigma)$. Whereas the
nonrotating solution implies the AH coefficient to be vanishing, and thus
nonrotating electric and magnetic fields to be either parallel or antiparallel,
the relative orientation of rotating electric and magnetic fields and the
evolution of the CM conductivity $\kappa_{B}$ are strongly affected by
nonvanishing $\kappa_{E}$. We explore the effect of positive and negative
$\omega_{0}$ on the evolution of the CM current, and show, in particular, that
a rotation of electromagnetic fields with negative $\omega_{0}$ implies a sign
flip of the CM current in a chiral fluid with nonvanishing AH current.
