Turbulent thermal superstructures in Rayleigh-Bénard convection

Abstract

We report the observation of superstructures, i.e. very large-scale and long living coherent structures in highly turbulent Rayleigh-Bénard convection up to Rayleigh Ra = 10 9 . We perform direct numerical simulations in horizontally periodic domains with aspect ratios up to Γ = 128. In the considered Ra number regime the thermal superstructures have a horizontal extend of six to seven times the height of the domain and their size is independent of Ra. Many laboratory experiments and numerical simulations have focused on small aspect ratio cells in order to achieve the highest possible Ra. However, here we show that for very high Ra integral quantities such as the Nusselt number and volume averaged Reynolds number only converge to the large aspect ratio limit around Γ ≈ 4, while horizontally averaged statistics such as standard deviation and kurtosis converge around Γ ≈ 8, and the integral scale converges around Γ ≈ 32, and the peak position of the temperature variance and turbulent kinetic energy spectra only around Γ ≈ 64.

Coherence of temperature and velocity superstructures in turbulent Rayleigh–Bénard flow

“…Moreover, the correlation between the two quantities appears much lower than one would naively expect, given that the temperature fluctuations provide the driving of w. These observations seem at odds with the notion that superstructures in RBC form large-scale convection rolls for which temperature and velocity scales should be of the same size. To address and clarify this issue along with related questions, we use the dataset of Stevens et al (2018) to assess energy distributions and coherence on a scale-by-scale basis. Before presenting our results in §3, we provide the relevant details on the dataset of Stevens et al (2018), together with the parameters of additional simulations performed for this study, in §2.…”

Large-Scale Pattern Formation in the Presence of Small-Scale Random Advection

“…This allowed the detailed investigation of the role of fluctuations on the emergence of patterns, which cannot be directly studied in RBC. With turbulent diffusion leading to a larger wavelength of the emerging pattern, our model offers a qualitative explanation for the wavelength growth of the turbulent superstructures with an increasing Rayleigh number [14,17,18]. Therefore, the presented results may guide future quantitative investigations of the role of turbulent fluctuations in RBC and other turbulent flows with emergent large-scale patterns.…”

“…As a prototypical model for the emergence of large-scale patterns in convection, we illustrate our findings at the example of the Swift-Hohenberg (SH) equation [30], which we generalize to feature random advection. We find that random advection shifts the onset of pattern formation and effectively increases the pattern's wavelength by turbulent diffusion, offering a qualitative explanation for recent observations in turbulent RBC [17,18].To start with, we consider a scalar order parameter field θ(x, t) that exhibits pattern formation in two dimensions. Its nondimensionalized evolution equation takes the formHere, L and N denote linear and nonlinear opera-arXiv:1909.10814v1 [physics.flu-dyn]…”

“…Both experiments and, in particular, numerical simulations have provided insights into these complex flow regimes [1][2][3]. Remarkably, coherent large-scale flow patterns, so-called turbulent superstructures, have been reported in the presence of small-scale turbulence [12][13][14][15][16][17][18]. Using suitable averaging techniques, the topology and dynamics of the superstructures have been extracted from the turbulent flow fields, demonstrating, e.g.,large-scale dynamics reminiscent of spiraldefect chaos [16].…”

A comparative evaluation of three volume rendering libraries for the visualization of sheared thermal convection

“…It has been previously shown in thermal convection that the large thermal plumes can be traced until very close to the heated and cooled plates [14]. So it is very important to also observe the emergence of structures close to the boundary layer.…”