Memory effects in the motion of a suspended particle in a turbulent fluid

The noninstantaneous behavior of the velocity correlation function for a turbulent fluid leads to memory effects in the equation of motion of a particle suspended in such a fluid. This effect is a direct consequence of the fluctuation-dissipation theorem, which connects the correlation properties of the random force with a memory function. As a result, the equation of motion of a suspended particle in a turbulent flow is an integro-differential rather than a differential equation, and the diffusion coefficient of a suspended particle and that of a fluid do not coincide even in the simplest model. The velocity correlation function of a particle and its diffusion coefficient are found for a simple model.