Enhancement of zonal flow damping due to resonant magnetic perturbations in the background of an equilibrium $E\times B$ sheared flow

Using a parametric interaction formalism, we show that the equilibrium sheared rotation can enhance the zonal flow damping effect found in Ref. [M. Leconte and P.H. Diamond, \emph{Phys. Plasmas} 19, 055903 (2012)]. This additional damping contribution is proportional to $(L_s/L_V)^2 \times \delta B_r^2 / B^2$,where$L_s/L_V$ is the ratio of magnetic shear length to the scale-length of equilibrium $E\times B$ flow shear, and $\delta B_r\mathrm{/}B$ is the amplitude of the external magnetic perturbation normalized to the background magnetic field.