Particle diffusion in a frozen isotropic 2D random velocity field is studied by simulation, and the results are compared with prediction of simple model. The model accounts for effects particle trapping infinite correlation time.

Since the cosmic peculiar velocity field depends on small wave-number modes strongly, we cannot probe its universal properties unless we observe a sufficiently large region. We calculate the expected deviation (sample variance) of the peculiar velocity dispersion from its universal value in the case observed volume is finite. Using linear theory we show that the sample variance remains as large...

In this note we study advection-diffusion equations associated to incompressible $$W^{1,p}$$ velocity fields with $$p>2$$ . We present new estimates on the energy dissipation rate and discuss applications of upper bounds enhanced rate, lower $$L^2$$ norm density, quantitative vanishing viscosity estimates. The key tools employed in our argument are a propagation regularity result, coming from t...