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

We report measurements of the temperature variance $\sigma^2(z,r)$ andfrequency power spectrum $P(f,z,r)$ ($z$ is the distance from the sample bottomand $r$ the radial coordinate) in turbulent Rayleigh-B\'enard convection (RBC)for Rayleigh numbers $\textrm{Ra} = 1.6\times10^{13}$ and $1.1\times10^{15}$and for a Prandtl number $\textrm{Pr} \simeq 0.8$ for a sample with a height $L= 224$ cm and aspect ratio $D/L = 0.50$ ($D$ is the diameter). For $z/L$ lessthan or similar to $0.1$ $\sigma^2(z,r)$ was consistent with a logarithmicdependence on $z$, and there was a universal (independent of $\textrm{Ra}$,$r$, and $z$) normalized spectrum which, for $0.02$ less than or similar to$f\tau_0$ less than or similar to $0.2$, had the form $P(f\tau_0) = P_0(f\tau_0)^{-1}$ with $P_0 =0.208 \pm 0.008$ a universal constant. Here $\tau_0= \sqrt{2R}$ where $R$ is the radius of curvature of the temperatureautocorrelation function $C(\tau)$ at $\tau = 0$. For $z/L \simeq 0.5$ themeasurements yielded $P(f\tau_0) \sim (f\tau_0)^{-\alpha}$ with $\alpha$ in therange from 3/2 to 5/3. All the results are similar to those for velocityfluctuations in shear flows at sufficiently large Reynolds numbers, suggestingthe possibility of an analogy between the flows that is yet to be determined indetail.

Logarithmic Spatial Variations and Universal $f^{-1}$ Power Spectra of Temperature Fluctuations in Turbulent Rayleigh-B\'enard Convection