Suppression of vertical diffusion in strongly stratified turbulence

A spectral approximation for diffusion of passive scalar in stably and strongly stratified turbulence is presented. The approximation is based on a linearized approximation for the Eulerian two-time correlation and Corrsin's conjecture for the Lagrangian two-time correlation. For strongly stratified turbulence, the vertical component of the turbulent velocity field is well approximated by a collection of Fourier modes (waves) each of which oscillates with a frequency depending on the direction of the wavevector. The proposed approximation suggests that the phase mixing among the Fourier modes having different frequencies causes the decay of the Lagrangian two-time vertical velocity autocorrelation, and the highly oscillatory nature of these modes results in the suppression of single-particle dispersion in the vertical direction. The approximation is free from any ad hoc adjusting parameter and shows that the suppression depends on the spectra of the velocity and fluctuating density fields. It is in good agreement with direct numerical simulations for strongly stratified turbulence.