Multiscale Statistics of Lagrangian and Eulerian Acceleration in Turbulent Stratified Shear Flows

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Direct numerical simulation data of homogeneous turbulence with shear and stratification are analyzed to study the Lagrangian and Eulerian acceleration statistics. Richardson numbers from $Ri=0$, corresponding to unstratified shear flow, to $Ri=1$, corresponding to strongly stratified shear flow, are considered. 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 exhibit a strong and similar influence on $Ri$. The extreme values for Lagrangian acceleration are weaker than those observed for the Eulerian acceleration. Similarly, the Lagrangian time-rate of change of fluctuating density is observed to have smaller extreme values than that of the Eulerian time-rate of change. Thus the time-rate of change of fluctuating density obtained at a fixed location is mainly due to advection of fluctuating density through this location. In contrast the time-rate of change of fluctuating density following a fluid particle is substantially smaller, and due to production and dissipation of fluctuating density.