Papers › Stochastic Lagrangian Dynamics of Vorticity. I. General Theory
Stochastic Lagrangian Dynamics of Vorticity. I. General Theory
Gregory L. Eyink, Akshat Gupta, Tamer Zaki
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
Prior mathematical work of Constantin and Iyer (2008, 2011) has shown that incompressible Navier-Stokes solutions possess infinitely-many stochastic Lagrangian conservation laws for vorticity, backward in time, which generalize the invariants of Cauchy (1815) for smooth Euler solutions. We simplify this theory for the case of wall-bounded flows by appealing to the Kuz'min (1983)-Oseledets (1989) representation of Navier-Stokes dynamics, in terms of the vortex-momentum density associated to a continuous distribution of infinitesimal vortex rings. The Constantin-Iyer theory provides an exact representation for vorticity at any interior point as an average over stochastic vorticity contributions transported from the wall. We discuss relations of this Lagrangian formulation with the Eulerian theory of Lighthill (1963)-Morton (1984) for vorticity generation at solid walls, and also with a statistical result of Taylor (1932)-Huggins (1994), which connects dissipative drag with organized cross-stream motion of vorticity and which is closely analogous to the "Josephson-Anderson relation" for quantum superfluids. We elaborate a Monte Carlo numerical Lagrangian scheme to calculate the stochastic Cauchy invariants and their statistics, given the Eulerian space-time velocity field. The method is validated using an online database of a turbulent channel-flow simulation (Graham et al. 2016), where conservation of the mean Cauchy invariant is verified for two selected buffer-layer events corresponding to an "ejection" and a "sweep". The variances of the stochastic Cauchy invariants grow exponentially backward in time, however, confirming earlier observations of Lagrangian chaos in channel-flow turbulence.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections