  We consider chiral magnetohydrodynamics, i.e. a finite-temperature system
where an axial $U(1)$ current is not conserved due to an Adler-Bell-Jackiw
anomaly saturated by the dynamical operator $F_{\mu\nu} \tilde{F}^{\mu\nu}$. We
express this anomaly in terms of the 1-form symmetry associated with magnetic
flux conservation and study its realization at finite temperature. We present
Euclidean generating functional and dissipative action approaches to the
dynamics and reproduce some aspects of chiral MHD phenomenology from an
effective theory viewpoint, including the chiral separation and magnetic
effects. We also discuss the construction of non-invertible axial symmetry
defect operators in our formalism.
