Numerical study of vertical dispersion by stratified turbulence

Numerical simulations are carried Out to investigate vertical fluid particle dispersion in uniformly stratified stationary turbulent flows. The results are compared with the analysis of Lindborg & Brethouwer (J. Fluid Mech., vol. 614, 2008, pp. 303-314), who derived long- and short-time relations for the mean square vertical displacement of fluid particles. Several direct numerical simulations (DNSs) with different degrees of stratification and different buoyancy Reynolds numbers are carried out to test the long-time relation = 2 epsilon(P)t/N-2. Here, epsilon(P) is the mean dissipation of turbulent potential energy; N is the Brunt-Vaisala frequency; and t is time. The DNSs show good agreement with this relation, with a weak dependence on the buoyancy Reynolds number. Simulations with hyperviscosity are carried out to test the relation = (1 + pi C-PL)2 epsilon(P)t/N-2, which should be valid for shorter time scales in the range N-1 << t << T, where T is the turbulent eddy turnover time. The results of the hyperviscosity simulations come closer to this prediction with C-PL about 3 with increasing stratification. However, even in the simulation with the strongest stratification the growth of is somewhat slower than linear in this regime. Based on the simulation results it is argued that the time scale determining the evolution Of is the eddy turnover time, T, rather than the buoyancy time scale N-1, as suggested in previous studies. The simulation results are also consistent with the prediction of Lindborg & Brethouwer (2008) that the nearly flat plateau Of observed at t similar to T should scale as 4E(P)/N-2, where E-P is the mean turbulent potential energy.