English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Quasi-stationary, or metastable, states play an important role intwo-dimensional turbulent fluid flows where they often emerge on time-scalesmuch shorter than the viscous time scale, and then dominate the dynamics forvery long time intervals. In this paper we propose a dynamical systemsexplanation of the metastability of an explicit family of solutions, referredto as bar states, of the two-dimensional incompressible Navier-Stokes equationon the torus. These states are physically relevant because they are associatedwith certain maximum entropy solutions of the Euler equations, and they havebeen observed as one type of metastable state in numerical studies oftwo-dimensional turbulence. For small viscosity (high Reynolds number), thesestates are quasi-stationary in the sense that they decay on the slow, viscoustimescale. Linearization about these states leads to a time-dependent operator.We show that if we approximate this operator by dropping a higher-order,non-local term, it produces a decay rate much faster than the viscous decayrate. We also provide numerical evidence that the same result holds for thefull linear operator, and that our theoretical results give the optimal decayrate in this setting.

Metastability and rapid convergence to quasi-stationary bar states for the 2D Navier-Stokes Equations