Lagrangian intermittencies in dynamic and static turbulent velocity fields from direct numerical simulations

Abstract

Three temporal velocity signals are analyzed from direct numerical simulations of the Navier–Stokes (N–S) equations. The three signals are: (i) the velocity of fluid particles transported by the time-evolving solution (Eulerian velocity field) of the N–S equations, referred to as the dynamic case; (ii) the velocity of fluid particles transported by a solution of the N–S equations at some fixed time, referred to as the static case; and (iii) the time evolution of the solution of the N–S equations at some fixed positions, referred to as the Eulerian case. The comparison of these three signals aims at elucidating the importance of the overall spacetime evolution of the flow on Lagrangian statistics. It is observed that the static case is, to some extent, similar to the Eulerian case; a feature that can be understood as an ergodicity property of homogeneous and isotropic turbulence and can be related to the process of random sweeping. The dynamic case is clearly different. It bears the signature of the time evolution of the flow. This study emphasizes the importance of the global dynamics of the flow and points out the existence of long-time correlations in the fluid-particle dynamics in the Lagrangian description.