Numerical simulations of particle dispersion in stratified flows

Abstract

Several researchers have examined the vertical dispersion of fluid particles in stratified flows to obtain a better understanding of mixing in geophysical flows. Pearson et al. [5] used a Langevin model to predict that the mean square of vertical fluid particle displacements reaches a plateau with $\langle\delta z^{2}\rangle \sim \langle w^{2}\rangle/N^2\ {\rm at}\ t \sim N^{-1}$ in stationary stratified flows. Here, w is the vertical velocity fluctuation and N is the Brunt-Väisälä frequency. At long times, they predict that $\langle\delta z^{2}\rangle \sim \langle w^{2} \rangle t/N$, when molecular diffusion alters the particle density. Venayagamoorthy and Stretch [6] examined the role of the changing particle density on vertical dispersion in DNS of decaying stratified turbulence and observed that after one eddy turnover time diabatic dispersion dominated. Van Aartrijk et al. [1] studied particle dispersion in DNS of stationary strat-ified turbulence and observed a plateau with $\langle\delta z^{2}\rangle \sim \langle w^{2} \rangle N^2\ {\rm at}\ t \sim N^{-1}$. However, some of the DNS showed that $\langle\delta z^{2}\rangle \sim t$ at long times caused by density changes of fluid particles by molecular diffusion.