“Stochasticity in Transitional and Fully-Developed Turbulence”

Nigel Goldenfeld (University of Illinois at Urbana-Champaign) will present at the 2022 Simons Collaboration on Wave Turbulence Annual Meeting on December 1st and 2nd in New York.

“Stochasticity in Transitional and Fully-Developed Turbulence”:

There is growing evidence that turbulence in simple fluids is governed by two fixed points arising in the statistical mechanical description of flows.  The first controls the behaviour near the laminar-turbulence transition, while the second controls the behaviour at asymptotically large Reynolds numbers.  In the first part of the talk, I review the phenomena associated with the sub-critical transition to turbulence, primarily in quasi-one-dimensional flows such as pipe or high aspect-ratio Taylor-Couette, and show how theory and experiment are converging on a description based on a non-equilibrium phase transition.  In particular, I present a stochastic model that captures decay and splitting of localised regions of turbulence (puffs), and the way in which regions of turbulence grow at higher Reynolds number, through two modes of growth (weak and strong slugs).  I also show how recent experimental measurements on puff dynamics, when combined with renormalization group and simulation methods, unequivocally supports the identification of laminar-turbulence transition of pipes in the directed percolation universality class.  In the second part of the talk, I discuss more briefly the widely unappreciated role of thermal fluctuations in the far dissipation range of turbulence, and using shell models, show how these are amplified and propagated to large scales by spontaneous stochasticity, reaching the integral scale eddies in just a few eddy turnover times.

Work performed in collaboration with: Hong-Yan Shih (UIUC/Academia Sinica, Taiwan), Xueying Wang (University of Illinois at Urbana-Champaign), Tsung-Lin Shieh (UIUC/Princeton), Bjorn Hof (Institute of Science and Technology, Austria), Joachim Matheson (Niels Bohr Institute, Denmark), Gregoire Lemoult (University of Le- Havre, France), Vasudevan Mukund (Institute of Science and Technology, Austria), Gaute Linga (Niels Bohr Institute), Dmytro Bandak (University of Illinois at Urbana-Champaign), Gregory Eyink (Johns Hopkins University), Alexei Mailybaev (IMPA, Brazil).

This work was partially supported by grants from the Simons Foundation through Targeted Grant “Revisiting the Turbulence Problem Using Statistical Mechanics” (Grant Nos. 663054 (G.E.), 662985 (N.G.) and 662960 (BH)).