Diffusion of a nearly spherical deformable body in a randomly stirred host fluid

The motion of a deformable body is investigated for cases in which the body is immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we show that the motion of its center is decoupled from its deformation degrees of freedom. We study the general case in which the velocity field, imposed on the system, is correlated both in space and time. We derive the mean-squared displacement of the body for the general random velocity field, and consider several useful cases including: white-noise flow, turbulence-like flow, and thermal agitation.