Turbulent dispersion in strongly stratified turbulence

The first part is the derivation of one-particle vertical diffusion for stably stratified turbulence with or without rapid rotation. Nicolleau & Vassilicos (2000) have analytically calculated vertical one-particle diffusion in stably stratified turbulence without rotation. One-particle vertical diffusion for turbulence with stable stratification and with or without rapid rotation has been derived here analytically using the solutions of the linearized equations of motions. The second part is an attempt to explain the depletion of horizontal pair diffusion in strongly stratified turbulence. "Recently, Nicolleau et al. (2005) have shown that in their Kinematic Simulations (KS) of vertically stably and strongly stratified homogeneous turbulence (Froude number smaller than 1). horizontal pair diffusion is significantly depleted by comparison to unstratified isotropic and homogeneous two- and three-dimensional turbulence. We have seeked to explain this depletion of horizontal pair diffusion by vertical stratification in terms of the probability density function of the horizontal divergence of the velocity field and the statistics of stagnation points following the recent approach to Richardson pair diffusion by Davila & Vassilicos (2003), Goto & Vassilicos (2004), Goto et al. (2005) and Osborne et al. (2005). We measure the number density of stagnation points in the KS of three-dimensional strongly stratified turbulence and find that it is virtually identical to what it is in KS of three-dimensional isotropic turbulence The third part is a study of the vertical motions of small, spherical inertial particles in strongly stratified turbulence.