We derive hydrodynamic equations for the point-spread function of an imaging system looking through atmospheric turbulence at an incoherent object. These are derived from the hydrodynamics of the index of refraction of the air. We use the path integral representation of the paraxial approximation for wave propagation through turbulence. We then study the case of a frozen turbulent refractive index field being advected past the imaging system with a constant wind and discuss the implications for optical flow estimation. We conclude by discussing possible directions for future work.