Predicting the Final Stationary State of Sheared 2D Euler Fluids
Abstract
The Kelvin-Helmholtz (KH) instability is a fundamental signature of the natural world, manifesting in phenomena ranging from atmospheric clouds to the iconic turbulence of Jupiter's Great Red Spot. While the linear dynamics of this instability is well-understood, the ultimate fate of the fluid --- the final stationary state to which it relaxes --- remains a formidable challenge. In this paper, we present a general non-equilibrium statistical mechanics framework that allows us to predict the asymptotic vorticity distribution of a sheared 2D Euler fluid. By constructing a self-consistent ansatz for the solution of the Vlasov equation, we determine the stationary stream function without explicitly solving the time-dependent Euler equations. We demonstrate that the relaxation leads to a population-inverted core, where high-energy states are fully occupied, surrounded by a tenuous halo of vortices in the lower-energy regions of configuration space. This result establishes the core-halo structure as a robust statistical consequence of the system's evolution, offering a universal framework for understanding the saturation of shear-induced turbulence in inviscid 2D fluids.
Versions
Related
- When hadrons collide: di-J/psi structure in the final state
- The ψ(2S) state as a subthreshold pole in electron positron annihilation into DD̅ final states
- Logarithmically-accurate final-state showers with massive quarks
- The decay ηc→ pp̅η with meson--baryon final-state interactions
- Discriminating baryonium and final-state-interaction interpretations of X(2356)
BibTeX
@misc{pakter2026predicting,
title = {{Predicting the Final Stationary State of Sheared 2D Euler Fluids}},
author = {Renato Pakter and Yan Levin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13615},
eprint = {2610.13615},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13615},
}
RIS
TY - UNPB
TI - Predicting the Final Stationary State of Sheared 2D Euler Fluids
AU - Renato Pakter
AU - Yan Levin
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13615
UR - https://arxiv.org/abs/2610.13615
AB - The Kelvin-Helmholtz (KH) instability is a fundamental signature of the natural world, manifesting in phenomena ranging from atmospheric clouds to the iconic turbulence of Jupiter's Great Red Spot. While the linear dynamics of this instability is well-understood, the ultimate fate of the fluid --- the final stationary state to which it relaxes --- remains a formidable challenge. In this paper, we present a general non-equilibrium statistical mechanics framework that allows us to predict the asymptotic vorticity distribution of a sheared 2D Euler fluid. By constructing a self-consistent ansatz for the solution of the Vlasov equation, we determine the stationary stream function without explicitly solving the time-dependent Euler equations. We demonstrate that the relaxation leads to a population-inverted core, where high-energy states are fully occupied, surrounded by a tenuous halo of vortices in the lower-energy regions of configuration space. This result establishes the core-halo structure as a robust statistical consequence of the system's evolution, offering a universal framework for understanding the saturation of shear-induced turbulence in inviscid 2D fluids.
ER -