Analysis of Lagrangian stretching in turbulent channel flow using a task-parallel particle tracking algorithm in the Johns Hopkins Turbulence Databases

Perry L. Johnson1, Stephen H. Hamilton2, Randal Burns2, Charles Meneveau1, [1] Department of Mechanical Engineering, Johns Hopkins University, [2] Department of Computer Science, Johns Hopkins University


The exponential deformation of fluid elements along Lagrangian paths is an intrinsic property of turbulent flows with importance in a wide variety of natural and engineering flows, such as droplet or bubble break-up, polymer-induced drag reduction, and device-induced hemolysis. The production of enstrophy by vorticity stretching, a dynamically important process in the turbulent energy cascade, follows from a similar mechanism in the Lagrangian view, though the alignment statistics differ and viscosity prevents unbounded growth. In this presentation, the stretching properties of fluid elements and vorticity along Lagrangian paths are studied using Direct Numerical Simulation (DNS) results channel flow at Reτ = 1000 and compared with results from isotropic turbulence. The Lagrangian analysis is performed using the Johns Hopkins Turbulence Databases (JHTDB), which contain time-resolved flow histories of the channel flow (~ 100 TB) and isotropic turbulence (~ 20 TB) simulations. A task-parallel algorithm, shown to be effcient compared to other approaches in the isotropic database, is extended to the case of flow in a bounded domain. It is shown that above 100 viscous units from the wall, stretching statistics are equal to their isotropic values, in support of the local isotropy hypothesis, which is central to our present understanding of high Reynolds number turbulent flows. In the viscous sublayer very close to the boundary, these stretching statistics approach values more consistent with an unsteady two-dimensional shear flow, in which exponential stretching no longer occurs. Normalized by dissipation rate, the stretching near the wall is less effcient due to less favorable alignment statistics. The Cramér function characterizing cumulative Lagrangian stretching statistics shows that overall the channel flow has about half of the stretching per unit dissipation compared with isotropic turbulence.