Confined Rayleigh-Bénard, Rotating Rayleigh-Bénard, and Double Diffusive Convection: A unifying view on turbulent transport enhancement through coherent structure manipulation
Kai Leong Chong, Yantao Yang, Shi-Di Huang, Jin-Qiang Zhong, Richard J. A. M. Stevens, Roberto Verzicco, Detlef Lohse, Ke-Qing Xia
备注：
10 pages, 5 figures, and 3 tables in main text and supplementary materials
Many natural and engineering systems are simultaneously subjected to a driving force and a stabilizing force. The interplay between the two forces, especially for highly nonlinear systems such as fluid flow, often results in surprising features. Here we reveal such features in three different types of Rayleigh-Bénard (RB) convection, i.e. buoyancy-driven flow with the fluid density being affected by a scalar field. In the three cases different {\it stabilizing forces} are considered, namely (i) horizontal confinement, (ii) rotation around a vertical axis, and (iii) a second stabilizing scalar field. Despite the very different nature of the stabilizing forces and the corresponding equations of motion, at moderate strength we counterintuitively but consistently observe an {\it enhancement} in the flux, even though the flow motion is weaker than the original RB flow. The flux enhancement occurs in an intermediate regime in which the stabilizing force is strong enough to alter the flow structures in the bulk to a more organised morphology, yet not too strong to severely suppress the flow motions. Near the optimal transport enhancements all three systems exhibit a transition from a state in which the thermal boundary layer (BL) is nested inside the momentum BL to the one with the thermal BL being thicker than the momentum BL.
We report experimental measurements of heat transport in rotating Rayleigh-B{é}nard convection in a cylindrical convection cell with aspect ratio $Γ= 1/2$. The fluid was helium gas with Prandtl number Pr = 0.7. The range of control parameters was Rayleigh number $4 \times 10^9 < {\rm Ra} < 4 \times 10^{11}$ and Ekman number $2 \times 10^{-7} < {\rm Ek} < 3 \times 10^{-5}$(corresponding to Taylor number $4 \times 10^9 < {\rm Ta} < 1 \times 10^{14}$ and convective Rossby number $0.07 < {\rm Ro} < 5$). We determine the crossover from weakly rotating turbulent convection to rotation dominated geos…
We report Particle Image Velocimetry of the Large Scale Circulation and the viscous boundary layer in turbulent thermal convection. We use two parallelepipedic Rayleigh-B{é}nard cells with a top smooth plate. The first one has a rough bottom plate and the second one has a smooth one so we compare the rough-smooth and the smooth-smooth configurations. The dimensions of the cell allow to consider a bi-dimensional mean flow. Lots of previous heat flux measurements have shown a Nusselt--Rayleigh regime transition corresponding to an increase of the heat flux in presence of roughness which is highe…
In agreement with a recent experimental discovery by Xia et. al. (2009), we also find a sloshing mode in experiments on the large-scale circulation (LSC) of turbulent Rayleigh-Benard convection in a cylindrical sample of aspect ratio one. The sloshing mode has the same frequency as the torsional oscillation discovered by Funfschilling and Ahlers (2004). We show that both modes can be described by an extension of a model developed previously [Brown and Ahlers (2008)] which consists of permitting a lateral displacement of the LSC circulation plane away from the vertical center line of the sample…
We experimentally test the effects of tilting a turbulent Rayleigh-B{é}nard convection cell on the dynamics of the large-scale circulation (LSC) orientation $θ_0$. The probability distribution of $θ_0$ is measured, and used to obtain a tilt-induced potential acting on $θ_0$, which is used in a low-dimensional model of diffusion of $θ_0$ in a potential. The form of the potential is sinusoidal in $θ_0$, and linear in tilt angle for small tilt angles, which is explained by a simple geometric model of the vector direction of the mean buoyancy force acting on the LSC. However, the magnitude of the …
We test the ability of a low-dimensional turbulence model to predict how dynamics of large-scale coherent structures such as convection rolls change in different cell geometries. We performed Rayleigh-Bénard convection experiments in a cubic container, in which there is a single convection roll known as the large-scale circulation (LSC). The model describes the motion of the orientation $θ_0$ of the LSC as diffusion in a potential which is predicted as a function of the shape of the cell from an approximate solutions of the Navier-Stokes equations. The model predicts advected oscillation modes…
Results from direct numerical simulations of vertical natural convection at Rayleigh numbers $1.0\times 10^5$-$1.0\times 10^9$ and Prandtl number $0.709$ support a generalised applicability of the Grossmann-Lohse (GL) theory, which was originally developed for horizontal natural (Rayleigh-B{é}nard) convection. In accordance with the GL theory, it is shown that the boundary-layer thicknesses of the velocity and temperature fields in vertical natural convection obey laminar-like Prandtl-Blasius-Pohlhausen scaling. Specifically, the normalised mean boundary-layer thicknesses scale with the $-1/2$…
We consider axisymmetric Boussinesq convection in a shallow cylinder radius, L, and depth, H (<< L), which rotates with angular velocity $Ω$ about its axis of symmetry aligned to the vertical. Constant heat flux boundary conditions, top and bottom, are adopted, for which the onset of instability occurs on a long horizontal length scale provided that $Ω$ is sufficiently small. We investigate the nonlinear development by well-established two-scale asymptotic expansion methods. Comparisons of the results with the direct numerical simulations (DNS) of the primitive governing equations are good at …
Boundary layers play an important role in controlling convective heat transfer. Their nature varies considerably between different application areas characterized by different boundary conditions, which hampers a uniform treatment. Here, we argue that, independent from boundary conditions, systematic dissipation measurements in Rayleigh-Bénard convection capture the relevant near-wall structures. By means of direct numerical simulations with varying Prandtl numbers, we demonstrate that such dissipation layers share central characteristics with classical boundary layers, but, in contrast to the…
We have developed novel instrumentation for making Lagrangian measurements of temperature in diverse fluid flows. A small neutrally buoyant capsule is equipped with on-board electronics which measure temperature and transmit the data via a wireless radio frequency link to a desktop computer. The device has 80 dB dynamic range, resolving milli-Kelvin changes in temperature with up to 100 ms sampling time. The capabilities of these "smart particles" are demonstrated in turbulent thermal convection in water. We measure temperature variations as the particle is advected by the convective motion, a…
We conduct direct numerical simulations for turbulent Rayleigh-Bénard (RB) convection, driven simultaneously by two scalar components (say, temperature and salt concentration) with different molecular diffusivities, and measure the respective fluxes and the Reynolds number. To account for the results, we generalize the Grossmann-Lohse theory for traditional RB convections~(Grossmann and Lohse, J. Fluid Mech., 407, 27-56; Phys. Rev. Lett., 86, 3316-3319; Stevens et al., J. Fluid Mech., 730, 295-308) to this two-scalar turbulent convection. Our numerical results suggest that the generalized theo…
We offer a unifying theory for turbulent purely internally heated convection, generalizing the unifying theories of Grossmann and Lohse (2000, 2001) for Rayleigh--Bénard turbulence and of Shishkina, Grossmann and Lohse (2016) for turbulent horizontal convection, which are both based on the splitting of the kinetic and thermal dissipation rates in respective boundary and bulk contributions. We obtain the mean temperature of the system and the Reynolds number (which are the response parameters) as function of the control parameters, namely the internal thermal driving strength (called, when nond…
It is shown, using results of direct numerical simulations, that the spontaneous breaking of local reflectional symmetry (and corresponding localized kinetic and magnetic helicities) can dominate chaotic dynamics of the small-scale MHD dynamo in the Rayleigh-B{é}nard convection, in kinetically forced flows under strong stratification, in the near-surface solar convection, and in kinetically forced flows at large magnetic Reynolds numbers. The notions of deterministic and helical distributed chaos have been used for this purpose. The coexistence of large- and small-scale dynamo mechanisms and a…
A challenge in fundamental physics and especially in thermodynamics is to understand emergent order in far-from-equilibrium systems. While at equilibrium, temperature plays the role of a key thermodynamic variable whose uniformity in space and time defines the equilibrium state the system is in, this is not the case in a far-from-equilibrium driven system. When energy flows through a finite system at steady-state, temperature takes on a time-independent but spatially varying character. In this study, the convection patterns of a Rayleigh-B{é}nard fluid cell at steady-state is used as a prototy…
Numerical simulation studies in 2D with the addition of noise are reported for the convection of a supercritical fluid,3He, in a Rayleigh-Be'nard cell where the fluid parameters and cell height L are the same as in published laboratory experiments. The noise addition is to accelerate the instability onset after starting the heat flow across the fluid, so as to bring simulations into better agreement with experimental observations. Homogeneous temperature noise and spatial lateral periodic temperature variations in the top plate were programmed into the simulations. A speed-up in the instabilit…
The unifying theory of scaling in thermal convection (Grossmann & Lohse (2000)) (henceforth the GL theory) suggests that there are no pure power laws for the Nusselt and Reynolds numbers as function of the Rayleigh and Prandtl numbers in the experimentally accessible parameter regime. In Grossmann & Lohse (2001) the dimensionless parameters of the theory were fitted to 155 experimental data points by Ahlers & Xu (2001) in the regime $3\times 10^7 \le Ra \le 3 \times 10^{9}$ and $4\le Pr \le 34$ and Grossmann & Lohse (2002) used the experimental data point from Qiu & Tong (2001) and the fact th…
Université Paris-Saclay, CNRS（巴黎萨克雷大学，法国国家科学研究中心）；Technical University of Munich（慕尼黑工业大学）；Sorbonne Université（索邦大学）
Recent works have explored the potential of machine learning as data-driven turbulence closures for RANS and LES techniques. Beyond these advances, the high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of discretization of the underlying operators very much connected to the flow scales resolution, is capable of sustaining high levels of turbulence characterized by multi-scale features? We investigate the use of PINNs sur…
We present observations of oscillations in the shape of the temperature profile of the large-scale circulation (LSC) of turbulent Rayleigh-B{é}nard convection. Temperature measurements are broken down into Fourier moments as a function of $θ-θ_0$, where $θ$ is the azimuthal angle in a horizontal plane at mid-height, and $θ_0$ is the LSC orientation. The oscillation structure is dominated by a 3rd order sine moment and 3rd order cosine moment in a cubic cell. In contrast, these moments are not found to oscillate in a cylindrical cell. This geometry-dependent behavior can be explained by a model…
Double diffusive convection (DDC), which is the buoyancy driven flow with fluid density depending on two scalar components, is ubiquitous in many natural and engineering enviroments. Of great interests are scalers transfer rate and flow structures. Here we systematically investigate DDC flow between two horizontal plates, driven by an unstable salinity gradient and stabilized by a temperature gradient. Counterintuitively, when increasing the stabilizing temperature gradient, the salinity flux first increases, even though the velocity monotonically decreases, before it finally breaks down to th…
