Multiple States in Turbulent Large-Aspect-Ratio Thermal Convection: What Determines the Number of Convection Rolls?

Toward accelerated data-driven Rayleigh-Bénard convection simulations

A hybrid data-driven/finite volume method for 2D and 3D thermal convective flows is introduced. The approach relies on a single-step loss, convolutional neural network that is active only in the near-wall region of the flow. We demonstrate that the method significantly reduces errors in the prediction of the heat flux over the long-time horizon and increases pointwise accuracy in coarse simulations, when compared to direct computations on the same grids with and without a traditional subgrid model. We trace the success of our machine learning model to the choice of the training procedure, incorporating both the temporal flow development and distributional bias.

Tuning heat transport via coherent structure manipulation: recent advances in thermal turbulence

Tuning transport properties through the manipulation of elementary structures has achieved great success in many areas, such as condensed matter physics. However, the ability to manipulate coherent structures in turbulent flows is much less explored. This article reviews a recently discovered mechanism of tuning turbulent heat transport via coherent structure manipulation. We first show how this mechanism can be realized by applying simple geometrical confinement to a classical thermally driven turbulence, which leads to the condensation of elementary coherent structures and significant heat-transport enhancement, despite the resultant slower flow. Some potential applications of this new paradigm in passive heat management are also discussed. We then explain how the heat transport behaviors in seemingly different turbulence systems can be understood by this unified framework of coherent structure manipulation. Several future directions in this research area are also outlined.

Experimental study on the flow structures and dynamics of turbulent Rayleigh-Bénard convection in an annular cell

We conduct an experimental study on the flow structures and dynamics of turbulent Rayleigh-Bénard convection in an annular cell with radius ratio η≃0.5 and aspect ratio Γ≃4. The working fluid is water with a Prandtl number of Pr≃5.4, and the Rayleigh number (Ra) ranges from 5.05×10^{7} to 5.05×10^{8}. The multithermal-probe method and the particle image velocimetry technique are employed to measure the temperature profiles and the velocity fields, respectively. Two distinct states with multiroll standing waves are observed, which are the quadrupole state (QS) characterized by a four-roll structure and the sextupole state (SS) by a six-roll structure. The scaling exponents of Reynolds number Re with Ra are different for the two states, which are 0.56 for QS and 0.41 for SS. In addition, the standing waves become unstable upon tilting the cell by 1^{∘} in relation to the horizontal plane, and they evolve into traveling waves. At relatively high Ra, for instance, Ra⩾2.55×10^{8}, it is observed that the traveling wave state SS undergoes a transition to the traveling wave state QS. However, the opposite transition from QS to SS is not observed in our experiments. Our findings provide insights into the flow structures and dynamics in the convection flow with rotation symmetry.

Experimental Evidence for the Existence of the Ultimate Regime in Rapidly Rotating Turbulent Thermal Convection

What is the final state of turbulence when the driving parameter approaches infinity? For the traditional Rayleigh-Bénard convection, a possible ultimate scaling dependence of the heat transport (quantified by the Nusselt number Nu) on the Rayleigh number (Ra), which can be extrapolated to arbitrarily high Ra, is predicted by theories. The existence of the ultimate scaling has been intensively debated in the past decades. In this Letter, we adopt a novel supergravitational thermal convection experimental setup to study the possible transition to the ultimate regime. This system is characterized by the combined effects of radial-dependent centrifugal force, the Earth's gravity, and the Coriolis force. With an effective gravity up to 100 times the Earth's gravity, both Ra and shear Reynolds number can be boosted due to the increase of the buoyancy driving and the additional Coriolis forces. With over a decade of Ra range, we demonstrate the existence of ultimate regime with four direct evidences: the ultimate scaling dependence of Nu versus Ra; the appearance of the turbulent velocity boundary layer profile; the enhanced strength of the shear Reynolds number; and the new statistical properties of local temperature fluctuations. The present findings will greatly improve the understanding of the flow dynamics in geophysical and astrophysical flows.

Molecular hints of two-step transition to convective flow via streamline percolation

Convection is a key transport phenomenon important in many different areas, from hydrodynamics and ocean circulation to planetary atmospheres or stellar physics. However, its microscopic understanding still remains challenging. Here we numerically investigate the onset of convective flow in a compressible (non-Oberbeck-Boussinesq) hard disk fluid under a temperature gradient in a gravitational field. We uncover a surprising two-step transition scenario with two different critical temperatures. When the bottom plate temperature reaches a first threshold, convection kicks in (as shown by a structured velocity field) but gravity results in hindered heat transport as compared to the gravity-free case. It is at a second (higher) temperature that a percolation transition of advection zones connecting the hot and cold plates triggers efficient convective heat transport. Interestingly, this picture for the convection instability opens the door to unknown piecewise-continuous solutions to the Navier-Stokes equations.

Rayleigh-Bénard convection with thermal boundary inhomogeneities

Rayleigh-Bénard convection with nonhomogeneous thermal boundaries (sinusoidal temperature patterns set in-phase at the top and bottom plates) is numerically studied in three- and two-dimensional domains. Two spatial convective scales occur: the one due to the self-organized clustering of plumes-which is known to appear in homogeneous conditions-and the scale induced by the boundary heterogeneities. The latter drives the convection patterning, both in 3D and 2D, when the wavelength of the perturbation is comparable with the self-organized one.