Turbulent superstructures in Rayleigh-Bénard convection

Abstract

Turbulent Rayleigh-Bénard convection displays a large-scale order in the form of rolls and cells on lengths larger than the layer height once the fluctuations of temperature and velocity are removed. These turbulent superstructures are reminiscent of the patterns close to the onset of convection. Here we report numerical simulations of turbulent convection in fluids at different Prandtl number ranging from 0.005 to 70 and for Rayleigh numbers up to 107. We identify characteristic scales and times that separate the fast, small-scale turbulent fluctuations from the gradually changing large-scale superstructures. The characteristic scales of the large-scale patterns, which change with Prandtl and Rayleigh number, are also correlated with the boundary layer dynamics, and in particular the clustering of thermal plumes at the top and bottom plates. Our analysis suggests a scale separation and thus the existence of a simplified description of the turbulent superstructures in geo- and astrophysical settings.

Convection‐Flow‐Assisted Preparation of a Strong Electron Dopant, Benzyl Viologen, for Surface‐Charge Transfer Doping of Molybdenum Disulfide

“…where g, β, v, α, and L are the acceleration of gravity, the thermal expansion coefficient, the kinematic viscosity, the thermal diffusivity, and the system length, respectively. The critical Ra is known to be 1,708; above that point, the instability and the convection flow is generated. Figure S5 shows the estimated Ra vs. Δ T curve in water, and that the convection flow would be generated even with a small temperature distribution (Δ T over ∼0.03 °C from equation (1)).…”

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

“…It has to be long enough in order to remove the small-scale fluctuations but significantly shorter than the time scale on which the largescale pattern evolves. This is similar to the procedure applied to Rayleigh-Bénard convection [16,18]. Example snapshots and averaged fields for different r are shown in Fig.…”

“…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]…”

“…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]. Extensive experimental and numerical investigations revealed that the length scale of the emerging patterns increases as a function of Rayleigh and Prandtl numbers as the flow becomes increasingly unsteady [19][20][21] and, finally, turbulent [14,18]. Investigations of RBC close to onset suggest that there is no universal scale selection mechanism, see, e.g., [22,23] for an overview.…”

“…By including random advection, we introduce a model for the fast, turbulent modes to the dynamics. The main motivation for this approach is the observation that the time-averaged patterns in the turbulent regime in RBC are reminiscent of the patterns close to onset, despite the presence of fluctuations [16][17][18]. Therefore the underlying assumption is that a description in terms of an order parameter field, superposed by fluctuations, remains valid in the turbulent case.…”