ON ACCELERATION STATISTICS IN TURBULENT STRATIFIED SHEAR FLOWS

Abstract

The Lagrangian and Eulerian acceleration statistics in homogeneous turbulence with uniform shear and 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 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. A consideration of the terms in the NavierStokes equation shows that the Lagrangian acceleration is mainly determined by the pressure-gradient, while the Eulerian acceleration is dominated by the nonlinear term. 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 due to the nonlinear term in the advection-diffusion equation for fluctuating density. 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. INTRODUCTION An understanding of the Lagrangian acceleration properties of a fluid particle in turbulent flows is of fundamental importance. After early work by Heisenberg (1948) and Yaglom (1949), recent studies range from theoretical investigations (e.g. Tsinober, 2001) to applications such as the modeling of particle dispersion (e.g. Pope, 1994). This work is carried out using both experimental (e.g. La Porta et al., 2001) as well as computational (e.g. Yeung, 2002; Toschi & Bodenschatz, 2009) approaches. The majority of previous investigations focused on Lagrangian properties of isotropic turbulence. The Lagrangian acceleration was found to be strongly intermittent and heavy tails were observed in its pdf. For example, extreme values as high as 1,500 times the acceleration of gravity were observed for the Lagrangian acceleration of fluid particles (La Porta et al., 2001) and numerical simulations confirmed these results (Toschi & Bodenschatz, 2009). Many applications of Lagrangian dynamics target the transport and mixing of natural and anthropogenic substances in the geophysical environment. Such flows are often characterized by the presence of shear and stratification. Homogeneous turbulent stratified shear flow with constant vertical stratification rate Sρ = ∂ρ/∂y and constant vertical shear rate S = ∂U/∂y represents the simplest flow configuration in order to study the competing effects of shear and stratification. This flow has been investigated extensively in the past: Experimental studies include Komori et al. (1983), Rohr et al. (1988), Piccirillo & Van Atta (1997), and Keller & Van Atta (2000). Numerical simulations include the work by Gerz et al. (1989), Holt et al. (1992), Jacobitz et al. (1997), and Jacobitz (2002). The goal of this work is to investigate the acceleration statistics in turbulent stratified shear flows using direct numerical simulations. In the following, the numerical approach taken is introduced first. Then, the Richardson number dependence of the Lagrangian and Eulerian acceleration pdfs are presented, followed by a discussion of the corresponding Lagrangian and Eulerian time-rate of change pdfs for the density field. APPROACH The mean flow considered in this study has a constant vertical shear rate S and a constant vertical stratification rate Sρ : U = Sy, V =W = 0, ρ = ρ0 +Sρ y (1) 1 June 30 July 3, 2015 Melbourne, Australia 9 3C-4