The super long-time decay of velocity fluctuations in a two-dimensional fluid

Abstract

We have calculated the velocity autocorrelation function for a tracer particle in a model two-dimensional fluid. The fluid was represented by a lattice Boltzmann equation with imposed fluctuations. By choosing a low Boltzmann diffusion coefficient for the tracer, the diverging contribution to the diffusion coefficient can be made to exceed the Boltzmann value even at short times. We were thus able to find evidence for the renormalized, or ‘super long-time’, decay of the VACF in a two-dimensional fluid. We find quantitative evidence for the 1/t√ln(t) decay predicted by theory.