  We consider Brownian particles immersed in the fluid which flow is turbulent.
We study the limit where the particles' inertia is weak and their velocity
relaxes fast to the velocity of the flow. The trajectories of the particles in
this case have a strange attractor in the physical space, if the particles'
diffusion is neglected. Under the latter condition the singular density of the
particles was recently described completely. The analysis was done for real
turbulence and did not involve the flow modeling. Here we take the diffusion
into account showing how it modifies the statistics. The analysis is performed
also for real turbulence. Experimentally testable predictions are made.
