Lagrangian and Eulerian accelerations in turbulent stratified shear flows

TL;DR

This study investigates the properties of Lagrangian and Eulerian accelerations in turbulent stratified shear flows using direct numerical simulations, revealing their statistical behaviors, scale dependence, and underlying physical mechanisms across different stratification levels.

Contribution

It provides a detailed analysis of acceleration statistics in stratified turbulence, highlighting differences between Lagrangian and Eulerian perspectives and their dependence on stratification and scale.

Findings

Eulerian acceleration exhibits stronger extreme values than Lagrangian acceleration.

Acceleration probability density functions become heavier-tailed at smaller scales, indicating increased intermittency.

Lagrangian acceleration is mainly influenced by pressure-gradient forces, while Eulerian acceleration is dominated by nonlinear convection.

Abstract

The Lagrangian (LA) and Eulerian Acceleration (EA) properties of fluid particles in homogeneous turbulence with uniform shear and uniform stable 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. The probability density functions (pdfs) of both LA and EA have a stretched-exponential shape and they show a strong and similar influence on the Richardson number. The extreme values of the EA are stronger than those observed for the LA. Geometrical statistics explain that the magnitude of the EA is larger than its Lagrangian counterpart due to the mutual cancellation of the Eulerian and convective acceleration, as both vectors statistically show an anti-parallel preference. A wavelet-based scale-dependent decomposition of the LA and EA is performed. The tails of the acceleration pdfs grow heavier for smaller scales of turbulent motion. Hence the flatness increases with decreasing scale, indicating stronger intermittency at smaller scales. The joint pdfs of the LA and EA indicate a trend to stronger correlations with increasing Richardson number and at larger scales of the turbulent motion. A consideration of the terms in the Navier--Stokes equation shows that the LA is mainly determined by the pressure-gradient term, while the EA is dominated by the nonlinear convection term.