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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Recent findings suggest that wall-bounded turbulent flow can take differentstatistically stationary turbulent states, with different transport properties,even for the very same values of the control parameters. What state the systemtakes depends on the initial conditions. Here we analyze the multiple states inlarge-aspect ratio ($\Gamma$) two-dimensional turbulent Rayleigh--B\'enard flowwith no-slip plates and horizontally periodic boundary conditions as modelsystem. We determine the number $n$ of convection rolls, their mean aspectratios $\Gamma_r = \Gamma /n$, and the corresponding transport properties ofthe flow (i.e., the Nusselt number $Nu$), as function of the control parametersRayleigh ($Ra$) and Prandtl number. The effective scaling exponent $\beta$ in$Nu \sim Ra^\beta$ is found to depend on the realized state and thus$\Gamma_r$, with a larger value for the smaller $\Gamma_r$. By making use of ageneralized Friedrichs inequality, we show that the elliptical instability andviscous damping determine the $\Gamma_r$-window for the realizable turbulentstates. The theoretical results are in excellent agreement with our numericalfinding $2/3 \le \Gamma_r \le 4/3$, where the lower threshold is approached forthe larger $Ra$. Finally, we show that the theoretical approach to frame$\Gamma_r$ also works for free-slip boundary conditions.

Multiple states in turbulent large-aspect ratio thermal convection: What determines the number of convection rolls?