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

In turbulent Rayleigh-B\'{e}nard (RB) convection, a transition to theso-called ultimate regime, in which the boundary layers (BL) are of turbulenttype, has been postulated. Indeed, at very large Rayleigh number $Ra \approx10^{13}-10^{14}$ a transition in the scaling of the global Nusselt number $Nu$(the dimensionless heat transfer) and the Reynolds number with $Ra$ has beenobserved in experiments and very recently in direct numerical simulations (DNS)of two-dimensional (2D) RB. In this paper we analyse the local scalingproperties of the lateral temperature structure functions in the BLs of thissimulation of 2D RB, employing extended self-similarity (ESS) (i.e., plottingthe structure functions against each other, rather than only against the scale)in the spirit of the attached eddy hypothesis, as we have recently introducedfor velocity structure functions in wall turbulence (Krug \textit{et al.},\textit{J. Fluid Mech.}, vol. 830, 2017, pp. 797-819). We find no ESS scalingbelow the transition and in the near wall region. However, beyond thetransition and for large enough wall distance $z^+ > 100$, we find clear ESSbehaviour, as expected for a scalar in a turbulent boundary layer. In strikingcorrespondence to the $Nu$ scaling, the ESS scaling region is negligible at $Ra= 10^{11}$ and well developed at $Ra = 10^{14}$, thus providing strong evidencethat the observed transition in the global Nusselt number at $Ra \approx10^{13}$ indeed is the transition from a laminar type BL to a turbulent typeBL. Our results further show that the relative slopes for scalar structurefunctions in the ESS scaling regime are the same as for their velocitycounterparts extending their previously established universality. The findingsare confirmed by comparing to scalar structure functions in 3D turbulentchannel flow.

journal of fluid mechanics

Transition to ultimate Rayleigh-B\'{e}nard turbulence revealed through  extended self similarity scaling analysis of the temperature structure  functions