Brownian motion in a rotating flow

The Langevin equations for a particle of an arbitrary shape and the correlation functions for the fluctuating forces, torques, or force-torque acting on the particle in a rotating flow are derived from the semimicroscopic level of coarse graining by using fluctuating hydrodynamics. In order to obtain the solution of the Navier-Stokes Langevin equation valid over the entire flow region, use is made of the method of matched asymptotic expansions in ( _f a²/v)^1/2 1. The cases of slow and rapid rotation are analyzed. It is shown that the fluctuation-dissipation theorems hold up to the order of ( _f a²/v)^1/2 in both slow and rapid rotation, and that the diffusivity tensor depends on the angular velocity of the fluid and becomes anisotropic.