Fluid dynamics of R-charged black holes

We construct electrically charged AdS5 black hole solutions whose charge, mass and boost-parameters vary slowly with the space-time coordinates. From the perspective of the dual theory, these are equivalent to hydrodynamic configurations with varying chemical potential, temperature and velocity fields. We compute the boundary theory transport coefficients associated with a derivative expansion of the energy momentum tensor and R-charge current up to second order. In particular, for the current we find a first order transport coefficient associated with the vorticity of the fluid.