  We modify the anomalous hydrodynamic equations of motion to account for
dissipative effects due to QCD sphaleron transitions. By investigating the
linearized hydrodynamic equations, we show that sphaleron transitions lead to
nontrivial effects on vector and axial charge transport phenomena in the
presence of a magnetic field. Due to the dissipative effects of sphaleron
transitions, a wavenumber threshold $k_{\rm CMW}$ emerges characterizing the
onset of chiral magnetic waves. Sphaleron damping also significantly impacts
the time evolution of both axial and vector charge perturbations in a QCD
plasma in the presence of a magnetic field. Based on our analysis of the
linearized hydrodynamic equations, we also investigate the dependence of the
vector charge separation on the sphaleron transition rate, which may have
implications for the experimental search for the Chiral Magnetic Effect in
Heavy Ion Collisions.
