Lagrangian and Eulerian Acceleration Statistics in Turbulent Stratified Shear Flows

The Lagrangian and Eulerian acceleration statistics in homogeneous turbulence with shear and stratification are studied using direct numerical simulations. The Richardson number is varied from $Ri=0$, corresponding to unstratified shear flow, to $Ri=1$, corresponding to strongly stratified shear flow. In addition, the scale dependence of the acceleration statistics is studied using a wavelet-based approach. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar influence on the Richardson number and extreme values for Eulerian acceleration are stronger than those observed for the Lagrangian acceleration. Similarly, the Eulerian time-rate of change of fluctuating density is observed to have larger extreme values than that of the Lagrangian time-rate of change. Hence, the time-rate of change of fluctuating density obtained at a fixed location by an Eulerian observer is mainly due to advection of fluctuating density through this location, while the time-rate of change of fluctuating density following a fluid particle is substantially smaller, and due to production and dissipation of fluctuating density.