Analysis of Lagrangian stretching in turbulent channel flow using a task-parallel particle tracking method in the Johns Hopkins Turbulence Databases Perry L. Johnson 1 , Stephen S. Hamilton 2 , Randal Burns 2 and Charles Meneveau 1 1 Department of Mechanical Engineering, Johns Hopkins University; 2 Department of Computer Science, Johns Hopkins University Johns Hopkins Turbulence Databases (JHTDB) I http://turbulence.pha.jhu.edu/ I access via web services I Fortran, C, Matlab, HDF5 cutout I built-in functions I e.g. getVelocity, getPressureHessian I interpolation & finite-differencing I Currently hosts four datasets: I Isotropic: 1024 3 × 5024 I Magnetohydrodynamics: 1024 4 I Channel: 2048 × 512 × 1536 × 4000 I Mixing: 1024 3 × 1012 Homogeneous Isotropic Turbulence vs. Turbulent Channel Flow incompressible Navier-Stokes: ∂ u i ∂ t + u j ∂ u i ∂ x j = - 1 ρ ∂ p ∂ x i + ν ∂ 2 u i ∂ x j ∂ x j + f i , ∂ u j ∂ x j = 0 I isotropic forcing in a periodic box I for studying small-scale turbulent motions I flow between infinite flat plates (u = 0 B.C.) I for studying turbulence near boundaries I Local isotropy hypothesis: zoom-in to any flow, statistically like isotropic turbulence Stretching of Fluid Elements and Vorticity x i ( t; X ,t 0 ) σ 1 σ 2 σ 3 X i ,t 0 D ij ( t; X ,t 0 )= ∂ x i ∂ X j dx i dt =u i ( x ,t ) dD ij dt = A ik D kj x i ( t; X ,t 0 ) X i ,t 0 dx i dt =u i ( x ,t ) ω i ( t 0 ) ω i ( t ) d ω i dt = A ij ω j +ν∇ 2 ω i I fluid elements and vorticity both stretched and rotated by same mechanism I BUT, different alignments with strain-rate → different stretching rates d σ i dt = b S (ii ) σ i where b S (ii ) is strain-rate along i th semi-axis σ 1 σ 2 σ 3 ^ S 11 ^ S 22 ^ S 33 ^ S ω ω d ω dt = b S ω ω where b S ω is strain-rate along vorticity axis Fluid Particle Tracking I Fluid particles follow the local flow velcity: ˙ x = u(x(t ), t ) I 2 nd -order method prevents particles from crossing physical boundaries Mediator Approach Task-Parallel Approach I Kanov & Burns (SC ‘15) showed that task-parallel approach is faster I here: implement for channel Stretching Rates: Mean Strength of strain-rate S ij ∼ τ -1 η varies with distance from boundary. τ η using bulk dissipation 10 0 10 1 10 2 10 3 y + 10 -3 10 -2 10 -1 10 0 | S (ii) |y + |τ η,bulk S 11 S 22 S 33 S ω I Peak stretching close to boundary: 10 < y + < 50 τ η using local dissipation 10 0 10 1 10 2 10 3 y + 10 -3 10 -2 10 -1 10 0 | S (ii) |y + |τ η S 11 S 22 S 33 S ω I Local isotropy in core: y + > 100 I Near boundary: less efficient I Investigate alignment between strain-rate and fluid element/vorticity. Stretching Rates: Full Probability Distribution All locations y + > 100, normalized by local dissipation. Fluid Elements -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 S (ii) τ η 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 Vorticity -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 S ω τ η 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 I More detailed support for local isotropy hypothesis in the core of the channel. Alignment with Strain-Rate: Mean 10 0 10 1 10 2 10 3 y + 0.0 0.2 0.4 0.6 0.8 1.0 cos 2 (θ 1j )|y + θ 11 θ 12 θ 13 10 0 10 1 10 2 10 3 y + 0.0 0.2 0.4 0.6 0.8 1.0 cos 2 (θ 3j )|y + θ 31 θ 32 θ 33 10 0 10 1 10 2 10 3 y + 0.0 0.2 0.4 0.6 0.8 1.0 cos 2 (θ 2j )|y + θ 21 θ 22 θ 23 10 0 10 1 10 2 10 3 y + 0.0 0.2 0.4 0.6 0.8 1.0 cos 2 (θ ωj )|y + θ ω1 θ ω2 θ ω3 Alignment with Strain-Rate: Full Probability Distribution 0.0 0.2 0.4 0.6 0.8 1.0 cos(θ 1j ) 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 cos(θ 3j ) 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 cos(θ 2j ) 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 cos(θ ωj ) 0 1 2 3 4 5 Conclusions I Local isotropy in core (y + > 100), less favorable alignments near the wall. I Overall, channel has 50% lower mean stretching rates per unit dissipation. Department of Mechanical Engineering - Johns Hopkins University - Baltimore, MD – [email protected] – http://turbulence.pha.jhu.edu/