Particle Diffusion in Stably Stratified Flows

Numerical simulations are used to study the vertical dispersion of fluid particles in homogeneous turbulent flows with a stable stratification. The results of direct numerical simulations are in good agreement with the relation for the long time fluid particle dispersion, <delta z(2)> = 2 epsilon(P)t / N-2, derived by [6], though with a small dependence on the buoyancy Reynolds number. Here, <delta z(2)> is the mean square vertical particle displacement, epsilon p is the dissipation of potential energy, t is time and N is the Brunt-Vaisala frequency. A simulation with hyperviscosicity is performed to verify the relation <delta z(2)> = (1 + pi C-PL)2 epsilon(P)t / N-2 for shorter times, also derived by [6]. The agreement is reasonable and we find that C-PL similar to 3. The onset of a plateau in <delta z(2)> is observed in the simulations at t similar to E-P / epsilon(P) which scales as 4E(P) / N-2, where E-P is the potential energy.