Session L33: Turbulent Convection II

Absence of evidence for transition to the 'ultimate' regime of Rayleigh-Bénard convection

There are several distinct predictions for the asymptotic behavior of heat transport Nu as the Rayleigh number Ra → ∞ in thermal turbulence described by the fundamental model of Rayleigh-Bénard convection. One is Nu = O(Ra^1/3) and another is the so-called 'ultimate' scaling Nu = O(Ra^1/2) possibly modified by logarithmic corrections to Ra^1/2/(log Ra)^3/2 or Ra^1/2/(log Ra)². Recently reported experimental and direct numerical simulation measurements of Nu as a function of Ra have been cited as evidence of transition to the 'ultimate' state. In this talk, without questioning the veracity of the Nu-Ra data reported therein, we show that the data do not support the claims.
  

Turbulent superstructures in Rayleigh-Bénard convection detected by deep learning

Turbulent convection in nature comprises vortices and plumes on many time and length scales that tend to assemble to gradually evolving large-scale patterns which are termed turbulent superstructures. These patterns appear in the form of ridge-like contours of hot upwelling and cold downwelling fluid. To detect them by machine learning techniques, we use a fully convolutional deep neural network that generates precise image segmentation from relatively small training sets. The neural network reduces the turbulent superstructures in an extended three-dimensional Rayleigh-Bénard convection layer to a planar network that connects defect points of the superstructure patterns. The dynamics of the network is manifest by the creation and annihilation of defects which determine the network topology. We estimate the fraction of heat transported across the network for varying Rayleigh numbers but fixed Prandtl number, and find the fraction to be significant.   

Transition of the Flow Reversal in Turbulent Thermal Convection

We present an experimental study on the flow reversals in quasi-2D turbulent Rayleigh-Benard convection. It is found the reversal rate decreases with Rayleigh number (Ra) and there is a transitional Ra, which separates the slow decease and fast decease regime of the reversal rate. Our velocity measurements show that for low Ra the interior of the main roll of the flow has already breaks into two small rolls although they are still enclosed by the envelope of the main roll, which is the reason for the frequent reversals for low Ra. In addition we decomposed the instantaneous flow field into Fourier modes and defined the stability of the single-roll mode, found that the stability of the single-roll mode experiences a slow increase followed by a fast increase. We believe this transition of the single-roll stability is responsible for the transition of the reversal rate. We also studied the Pr dependence of the transition and successfully revealed why reversal happens only in a restricted parameter ranges.   

Effects of boundary asymmetry in turbulent Rayleigh-Benard convection

We present study of the effects of boundary asymmetry in turbulent Rayleigh-Benard convection. This asymmetry was introduced by using roughness elements with different roughness aspect ratios λ on the top and the bottom plates, i.e., λ_t=1.0 (top plate) and λ_b=4.0 (bottom plate). The experiment was carried out in a cylindrical cell with an aspect ratio 1 and a diameter of 19.2 cm. The height of the roughness elements was 8 mm. The Rayleigh number Ra was in the range of 3.5×10⁸≤Ra≤ 8.2×10⁹ and the Prandtl number was Pr=4.34. It is found that the scaling exponents of the Nusselt number and the Reynolds number with Ra in the asymmetric cell is larger than those obtained in a symmetric cell with λ_t=λ_b=1.0 and smaller than those obtained in a symmetric cell with λ_t=λ_b=4.0. Measurement of the temperature profile along the cell's centerline suggests the boundary asymmetry not only changes the transport properties, but also leads to deviation of the mean temperature T_bulk from the averaged temperature of the top and bottom plate T_m. In addition, this deviation is Ra-dependent. The change of T_bulk might be due to the different plume dynamics at the asymmetric boundaries with increasing Ra.    

Radiatively heated thermal convection: bypassing the boundary layers to achieve the « ultimate » scaling regime.

The heat flux transported by thermal convection has important implications for geophysical, astrophysical and industrial flows: one seeks a power-law  relation between the convective heat flux and the internal temperature gradients. Decades of investigations of the Rayleigh-Bénard (RB) setup indicate that the heat transport is strongly restricted by boundary layers near the hot and cold solid plates. This prevents the observation of the “ultimate” scaling-regime of thermal convection, where bulk turbulence controls the convective heat flux independently of molecular viscosity and thermal diffusivity. In contrast with the RB setup, many geophysical and astrophysical convective flows are driven by radiation: absorption of incoming light by a body of fluid induces local heating. We have developed a laboratory experiment that reproduces such radiative heating: heat is input radiatively, directly inside the bulk turbulent flow and away from the boundary layers. We will provide experimental evidence that this naturally leads to the ultimate regime of thermal convection. These experimental results are confirmed quantitatively by Direct Numerical Simulations.