  We discuss the $(2+1)$-dimensional parity violating charged fluid on a finite
cutoff surface $\Sigma_c$, dual to the nondynamical and dynamical Chern-Simons
(CS) modified gravities. Using nonrelativistic long-wavelength expansion
method, the field equations are solved up to $\mathcal{O}(\epsilon^2)$ in the
nondynamical model. It is shown that there exists nonvortical dual fluid with
shear viscosity $\eta$ and Hall viscosity $\eta_A$ on the cutoff surface
$\Sigma_c$. The ratio of shear viscosity over entropy density $\eta/s$ of the
fluid takes the universal value $1/{4\pi}$, while the ratio of Hall viscosity
over entropy density $\eta_A/s$ depends on the $\Sigma_c$ and black brane
charge $q$. Moreover the nonvortical dual fluid obeys the magnetohydrodynamic
(MHD) equation. However, these kinematic viscosities $\nu$ and $\nu_A$ related
to $\eta$ and $\eta_A$ do not appear in this MHD equation, due to the
constraint condition $\tilde{\partial}^2\beta_j=0$ for the $(2+1)$-dimensional
dual fluid. Then, we extend our discussion to the dynamical CS modified gravity
and show that the dual vortical fluid possesses another so-called Curl
viscosity $\zeta_A$, whose ratio to entropy density $\zeta_A/s$ also depends on
the $\Sigma_c$ and $q$. Moreover, the value of $\eta/s$ still equals to
$1/4\pi$ and the result of $\eta_A/s$ agrees to the previous result under the
probe limit of the pseudo scalar field at the infinite boundary in the charged
black brane background for the dynamical CS modified gravity. This vortical
dual fluid corresponds to the magnetohydrodynamic (MHD) turbulence equation in
plasma physics.
