2018/08/26 by Fangying Song, George Em Karniadakis, Song, Fangying +1 · 1 citation
Engineering · Environmental Science · Physics and Astronomy · #76F10 #76F40 #76F70 #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Nanofluid Flow and Heat Transfer #Wind and Air Flow Studies #msc:76F10 #msc:76F40 #msc:76F70 #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.1808.10276
21 pages, 21 figures
arxiv created 2018/08/26 · openalex publication_date 2018/08/26 · arxiv updated 2018/08/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modeling of wall-bounded turbulent flows is still an open problem in classical physics, with only modest progress made in the last few decades beyond the so-called `log law', which describes only the intermediate region in wall-bounded turbulence, i.e., 30-50 y+ to 0.1-0.2 R+ (in wall units) in a pipe of radius R. Here we propose a fundamentally new approach based on fractional calculus to model the \em entire mean velocity profile from the wall to the centerline of the pipe. Specifically, we represent the Reynolds stresses with a non-local fractional derivative of \em variable order that decays with the distance from the wall. Surprisingly, we find that this variable fractional order has a universal form for all Reynolds numbers and for three different flow types, i.e., channel flow, Couette flow, and pipe flow. We first use existing data bases from direct numerical simulations (DNS) to learn the variable fractional order function, and subsequently we test it against other DNS data and experimental measurements, including the Princeton superpipe experiments. Taken together, our findings reveal the continuous and decaying change of rate of turbulent diffusion from the wall as well as the strong non-locality of turbulent interactions that intensify away from the wall.