Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session C16: Interact: Rotating and Non-Rotating Rayleigh-Benard Convection |
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Chair: Roberto Verzicco, University of Roma Tor Vergata Room: 155 F |
Sunday, November 24, 2024 10:50AM - 11:20AM |
C16.00001: INTERACT FLASH TALKS: Rotating and Non-Rotating Rayleigh-Benard Convection Each Interact Flash Talk will last around 1 minute, followed by around 30 seconds of transition time. |
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C16.00002: Helicity Production and Transfer in Rotating Convection Laura Currie, Joanne Mason, Steven Tobias Helicity is believed to be important in controlling the dynamics in many fluid systems and can arise through rotation, through shear flows, or by mechanical means. It gives a measure of broken reflectional symmetry in a flow. In naturally occurring systems, helicity is important in dynamo action since the breaking of reflectional symmetry is important for large scale magnetic field generation in electrically conducting flows. In these systems it is important to know which scales in the flow manifest a breaking of reflectional symmetry, as indicated by the degree of relative helicity at that scale. For this reason there has been a lot of interest in how helicity is produced and transported between scales but focus has often been on systems with a turbulence driven by forcing at a localised scale. However, in many natural systems, the production of helicity is not localised and can depend on the flow dynamics and potentially even on the helicity distribution itself. One such system of great importance for our understanding of stars and planets is rotating convection. In this talk I will examine the production and transport of helicity as a function of thermal driving and rotation rate in rotating convection. |
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C16.00003: Wavelength selection mechanism for turbulent superstructures in turbulent Rayleigh Bénard convection Fabian A Alvarez Garrido, Michael Wilczek Large-scale flow patterns are observed in Rayleigh-Bénard cells both close and far from the onset of convection. Experiments and direct numerical simulations reveal that the characteristic spatial scale of these structures significantly increases in the turbulent regime compared to the one at the onset of convection and grows with the Rayleigh number. Here, we propose a mechanism that can account for this departure. We model the effect of turbulent fluctuations on the heat transport of the large scales by introducing a height-dependent turbulent thermal diffusivity. Such a model is motivated by how the height dependence of the background temperature profile varies between the boundary layers and the bulk. We conduct a linear stability analysis and show that a gradient in the effective thermal diffusivity between the boundary layers and the bulk leads to an instability where the wavelength of the critical mode is higher than in a cell with homogeneous diffusivity. By linking the magnitude of this gradient with the Rayleigh number, we illustrate how an increase in the intensity of turbulent velocity fluctuations modifies the spatial scale of the turbulent superstructures. |
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C16.00004: Two-dimensional Rayleigh-Bénard convection in an annulus with radial gravity Abhiroop Bhadra, Olga Shishkina, Xiaojue Zhu Thermal convection in annulus domains with gravitational acceleration g that decreases with the radial coordinate r is commonly observed in astrophysical and geophysical flows. In these systems, the annulus radius ratio η is a control parameter, in addition to the Rayleigh number Ra and Prandtl number Pr. To study the effect of η, we conduct direct numerical simulations of Rayleigh-Bénard convection in a two-dimensional annulus. Keeping the inner shell hot and the outer shell cold, η is varied from 0.2 to 0.8, Ra from 107 to 1010, and Pr is kept constant at unity. The gravity profile assigned is g ∼ 1/r. For some parameter ranges, we observe zonal flows, which were not previously seen in systems without imposed external rotation. We demonstrate how the disproportionately strong inner plumes cause the zonal flow. Interestingly, the asymmetry in the properties of the inner and outer thermal boundary layers (TBLs) follows different scaling laws than those previously observed in three-dimensional systems. We develop scaling laws to quantify the asymmetry in the TBL widths and temperature drops in the inner and outer shells. By conditionally averaging the flow fields, we isolate the inner and outer plumes in the system and illustrate how the system’s curvature affects the boundary layer profiles. |
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C16.00005: Wall modes for conducting sidewall boundary conditions in rotating Rayleigh-Bénard convection Robert Everett Ecke, Xuan Zhang, Olga Shishkina Rotating Rayleigh-Bénard convection is a model experimental, computational, and theoretical system with which to help understand and characterize a broad range of natural phenomena. These involve rotation and buoyancy including fluid flows in the Earth’s atmosphere, oceans, and deep interior as well as in planetary atmospheres and in stars. The control parameters for rotating convection are the Rayleigh Number Ra ~ ΔT H3, the Ekman Number Ek ~ H-2/Ω, and the Prandtl Number Pr = ν/κ where ΔT is the temperature difference across a layer of height H, Ω is the angular rotation rate, ν is the kinematic viscosity, and κ is the thermal diffusivity. Numerous investigations have revealed bifurcations to wall localized states (wall modes) occurring at Rayleigh number Raw ~ Ek-1 [1] when the sidewalls are perfectly insulating or weakly thermally conducting. At higher Rac ~ Ek-4/3, bulk rotating convection begins [2] characterized for rapid rotation by a fascinating interplay of vortex states in near nonhydrostatic geostrophic balance. When the sidewalls are perfectly conducting, there is a distinct set of wall modes [3] that have very different properties and scalings compared to wall modes with perfectly insulating sidewalls. For example, one has an onset Rayleigh Number Rawc ~ Ek-4/3, the same as bulk mode scaling but with a smaller proportionality constant. We present direct numerical simulations of rapidly rotating Rayleigh-Bénard convection in small aspect ratio cylindrical convection cells with perfectly conducting boundary conditions for Pr = 0.8 and Ek = 10-6. We compare and contrast the properties of these conducting-boundary-condition wall modes with those for insulating sidewalls and discuss the importance of these states in experimental studies of rotating convection of compressed gases and cryogenic helium where sidewall conductivity is much greater than fluid conductivity. |
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C16.00006: Vorticity skewness of finite-amplitude rapidly rotating Rayleigh-Bénard convection Hao Fu, Shiwei Sun Rotating Rayleigh-Bénard convection denotes the convection between a warm plate and a cold plate in a rotating environment. It is a classic model for understanding convective vortices in the atmosphere and ocean. The influence of background rotation on fluid inertia breaks the symmetry between cyclones and anticyclones. Such a symmetry breaking could be represented by vorticity skewness, which still lacks a systematic theory. Rapidly rotating convection with stress-free boundaries and unit Prandtl number is a convenient starting point. The investigation starts from the convective onset stage, where the vortices grow stationarily. Asymptotic analysis shows that the volumetric vorticity skewness S is produced by the interaction between the n=0, 1, and n=1, 2 vertical eigenmodes. The n=0 (barotropic) mode positively contributes to S mainly by stretching the vertical relative vorticity, an ageostrophic effect. The n=2 mode makes a minor negative contribution to S by preferentially intensifying the outflow over the inflow, a non-hydrostatic effect. The theory predicts S to be proportional to the global Rossby number defined with the volumetric standard deviation of vorticity, Ro_g. The proportional factor does not depend on the Rayleigh and Ekman numbers, agreeing with direct numerical simulations. Then, the system enters the equilibrium stage. The stretching of vertical vorticity still dominantly contributes to S. At Ro_g ≥0.5, the emergent unsteady flow significantly suppresses the asymmetry between the inflow and outflow strength and weakens its influence on S. |
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C16.00007: Turbulent spherical Rayleigh--Bénard convection: Prandtl number dependence Yifeng Fu, Shujaut H. Bader, Xiaojue Zhu Direct numerical simulations (DNS) are performed to explore the Prandtl number (Pr) dependence of the turbulent Rayleigh--Bénard convection (RBC) in spherical shells. The simulations are performed for 0.1 ≤ Pr ≤ 10, radius ratio η = 0.2 and 0.6, and for a range of Rayleigh number (Ra) varying between 105 and 5 × 107. A centrally condensed gravity profile, g ∽ 1/r2, is employed in this study. Our primary aim is to analyze how Pr influences the global transport properties and flow physics. The scaling behavior of the Nusselt number (Nu) and Reynolds number (Re) with respect to Pr and Ra is investigated. It is observed that the asymmetry in the mean radial profiles of the temperature and velocity is a function of Pr and η. The asymmetry at smaller η has a stronger Pr dependence than at larger η. Various assumptions for quantifying this asymmetry are evaluated, revealing that different assumptions are valid at different Pr. It is shown that the assumption of the equivalency of local thermal boundary layer Rayleigh numbers holds only for Pr > 10. Furthermore, the assumption that the average plume density is the same at the inner and outer boundaries, as well as the assumption of the identical thermal scales between the two boundary layers, holds only for 0.2 < Pr < 1. Additionally, the validity of a new assumption based on the similarity of the average plume volume between the inner and the outer boundaries is proposed for Pr ≈ 0.1, which is validated using our DNS data. |
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C16.00008: Asymptotic scalings of steady rolls in Rayleigh-Bénard convection David Goluskin, Baole Wen, Greg P Chini In Rayleigh-Bénard convection, steady two-dimensional rolls are the simplest nonlinear states. They exist for all Rayleigh numbers (Ra) above the primary instability but are unstable at large Ra. The large-Ra asymptotic scalings of heat transport and other mean quantities are more accessible for steady rolls than for turbulence. Nonetheless, the possible scalings of steady rolls are surprisingly rich and not fully understood. Various scaling exponents are possible in the large-Ra limit, depending on the boundary conditions and on which simultaneous limit (if any) is taken in the aspect ratio of the rolls and/or the Prandtl number of the fluid. This talk will survey what is known about large-Ra limits of steady rolls at finite Prandtl numbers. For various asymptotic limits, we will show numerical computations of steady rolls with Ra as large as 1019, as well as matched asymptotic equations that are consistent with the numerical results. Depending on boundary conditions and on how the aspect ratio varies with Ra, the Nusselt number of steady rolls is predicted to scale like Raα with at least three different exponents that include α=1/3, 1/4, and 25/84. |
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C16.00009: Scaling for the latitudinal dependence of convection in the geostrophic regime Veeraraghavan Kannan, Xiaojue Zhu Turbulent convection, prevalent in various geophysical and astrophysical systems, significantly impacts heat transport, which is influenced by rotational forces. In this work, we investigate the rotating Rayleigh-Bénard convection paradigm, focusing on the less-explored effects of tilted rotation and gravity vectors to model low- and mid-latitude dynamics. Using direct numerical simulations in the geostrophic regime near onset, we systematically vary the latitude from 10° (near the equator) to 90° (poles) to examine the resulting flow structures and heat transport characteristics. Our findings reveal significant variations in flow patterns and heat transport efficiency with latitude, offering insights into length scale scaling with latitude, which are crucial for understanding the latitudinal scaling of heat (Nu) and momentum (Re) transport in the system. This study can help enhance our understanding of the latitudinal dependencies of convection, which are essential for improving climate and weather prediction models. |
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C16.00010: Dynamics of the thermal boundary layer in low Prandtl number Rayleigh–Bénard convection Nayoung Kim, Felix Schindler, Tobias Vogt, Sven Eckert The thermal and viscous boundary layers in Rayleigh–Bénard convection significantly influence global heat transport and large-scale flow structure. At low Prandtl numbers, the thermal boundary layer is thicker than the viscous layer due to differing diffusion rates. This study investigates the dynamics of the thermal boundary layer under low Pr conditions using a cylindrical cell filled with the eutectic alloy GaInSn, characterized by Pr ≈ 10-2, and Rayleigh numbers up to 109. Temperature profiles near the heating plate were measured using thermocouple arrays at the cell's centre and near the sidewall, representing shear and plume ejection regions. We reveal that the thermal boundary layer remains in a transient state, not fully transitioning to turbulence. Central profiles align with the Prandtl-Blasius profile, while sidewall profiles deviate. The shape factor of the temperature profile is consistently smaller than the Prandtl-Blasius profile across the entire range of Rayleigh numbers. Furthermore, thermal boundary layer thickness decreases with Ra, showing exponents of 0.26 in the plume ejection region and 0.2 in the shear region for a cell with an aspect ratio of 0.5. These findings deepen the understanding of thermal convection in liquid metals at low Prandtl numbers. |
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C16.00011: Role of Large-Scale Structures in the Correlation Between Temperature and Wall-Normal Velocity in Rayleigh-Bénard Convection Myoungkyu Lee Turbulent Rayleigh-Bénard convection is critical in scientific and engineering contexts, especially concerning the scaling of the Nusselt number (Nu) at high Rayleigh numbers (Ra). Direct numerical simulation (DNS) is a primary method for studying this phenomenon but achieving very high Ra with DNS is expensive. To address this, we conducted DNS with Ra up to 4×108, a Prandtl number (Pr) of 1, and a domain aspect ratio of 15. Our spectral analysis of wall-normal velocity and temperature covariance revealed that large-scale structures significantly influence these dynamics but have minimal impact on Nu scaling since these structures remain away from the wall and are not transferred to smaller scales. This suggests that small-domain DNS may inadequately represent large-scale structures for Nu scaling studies. Nevertheless, our findings indicate that using small domains has a limited impact on Nu, despite differences in the dynamics of the covariance. Given that dominant scale transfer from large to small scales was not observed, further investigation is needed to validate these results. |
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C16.00012: Supercritical and Subcritical Convection: Insights from Direct Numerical Simulation and Low-Dimensional Models in Rotating Systems Sutapa Mandal, Snehashish Sarkar, Pinaki Pal We explored the transition scenarios in rotating Rayleigh-B\'{e}nard convection with no-slip boundary conditions through 3D direct numerical simulations (DNS) and low-dimensional modeling. The governing parameters: Taylor number ($\mathrm{Ta}$), Rayleigh number ($\mathrm{Ra}$), and Prandtl number ($\mathrm{Pr}$) are varied within the ranges |
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C16.00013: Inverse cascade in zonal flows. Siddhant Mishra, Anikesh Pal Zonal winds on Jovian planets play an important role in governing the cloud dynamics, transport of momentum, scalars, and weather patterns. Therefore, it is crucial to understand the evolution of the zonal flows and their sustainability. Based on studies in two-dimensional (2D) β plane setups, zonal flow is believed to be forced at the intermediate scale via baroclinic instabilities, and the inverse cascade leads to the transfer of energy to large scales. However, whether such a process exists in three-dimensional (3D) deep convection systems remains an open and challenging question. To explore a possible answer, we perform Large Eddy Simulations at the geophysically interesting regime of Ra=1012, Ek=10-6,10-7 and 10-8 in horizontally rotating Rayleigh-Bénard convection setup and discover the existence of natural forcing through buoyancy and inverse cascade. The turbulent kinetic energy budget analysis and the spectral space assessment of the results corroborate the emanation of a strong mean flow from chaos. |
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C16.00014: Invariant solutions in homogeneous Rayleigh-Bénard convection Shingo Motoki, Genta Kawahara Thermal convection with boundary conditions in both horizontal and vertical directions, known as the homogeneous Rayleigh-Bénard convection, is a simple model for the bulk of convection cells, representing the ultimate turbulent state in which the vertical heat flux is independent of the thermal conductivity of fluids. In this system, however, exact solutions exponentially grow in time, leading to high intermittency in heat transfer and difficulties in stability and bifurcation analysis of the nonlinear dynamical system. We have found three-dimensional steady solutions to the Boussinesq equations for the homogeneous Rayleigh-Bénard convection, which bifurcate from a two-dimensional steady solution with a mirror symmetry about the horizontal plane, using a Newton-Krylov iteration. The nonlinear invariant solutions have hierarchical multiscale vortex structures and exhibit significantly higher heat flux than the two-dimensional steady solution. These solutions will help us better understand the homogeneous Rayleigh-Bénard convection and the conventional Rayleigh-Bénard convection. |
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C16.00015: Boundary layers in thermal convection are fluctuation-dominated Katepalli R Sreenivasan, Roshan J Samuel, Mathis Bode, Janet D Scheel, Joerg Schumacher We study the dynamics of thermal and momentum boundary regions in three-dimensional direct numerical simulations of Rayleigh-B\'{e}nard convection for the Rayleigh number range $10^5\le Ra \le 10^{11}$ and $Pr=0.7$. Using a Cartesian slab with horizontal periodic boundary conditions and an aspect ratio of 4, we obtain statistical homogeneity in the horizontal $x$- and $y$-directions, thus approximating an infinitely extended system. We also supplement these results by similar simulations for aspect ratios of 2 and 8 at $Ra = 10^9$. We observe upon canonical use of long-time and area averages, with averaging periods of at least 100 free-fall times, that a coherent mean flow is practically absent and that the magnitude of the velocity fluctuations is larger than the mean by up to 2 orders of magnitude. The velocity field close to the wall is a collection of differently oriented local shear-dominated patches interspersed with shear-free incoherent flow regions. The incoherent regions occupy a 60 % area fraction for all Rayleigh numbers. Rather than resulting in a pronounced mean with small fluctuations about this mean, the velocity field is dominated by strong fluctuations of all three components around a non-existent or weak mean. This feature is particularly pronounced for $Ra \ge 10^9$, which underlines the necessity for large aspect ratios and high Rayleigh numbers. We discuss the consequences of these observations for convection layers with larger aspect ratios, including boundary layer instabilities and the resulting turbulent heat transport. |
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C16.00016: Heat-transport-maximizing steady roll solutions in Rayleigh–Bénard convection Baole Wen, David Goluskin, Greg P Chini Steady two-dimensional convection rolls can transport heat at nearly the same rate as turbulent flows in Rayleigh–Bénard convection, despite the roll solutions being unstable at large Rayleigh numbers (Ra). This talk concerns the large-Ra asymptotic properties of steady roll solutions at various Prandtl numbers (Pr) between no-slip top and bottom boundaries. Waleffe et al. (Phys. Fluids 2015) and Sondak et al. (J. Fluid Mech. 2015) examined how the Nusselt number (Nu) of steady rolls depends on their horizontal period. At large Ra, they report two local maxima in Nu as a function of the period. Based on computations up to Ra ~ 109, they find that the global maximum of Nu occurs at the larger-period local maximum when Pr is less than approximately 7, but at the smaller-period local maximum when Pr is greater than about 7. Using new numerical methods, we compute steady roll solutions up to Ra values larger than 1014 for various Pr ≥ 1. Our computations seem to reach the large-Ra asymptotic regime, where there remain two local maxima of Nu, but where the global maximum of Nu always occurs at the larger-period local maximum for all Pr. These Nu-maximizing steady rolls achieve Nu ~ c Ra1/3—the so-called classical scaling. The large-Ra asymptotic structure of these Nu-maximizing roll solutions will be discussed. |
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C16.00017: Multiple states in Rayleigh-Bénard convection: A triad interaction manipulation framework Xiaojue Zhu, Rikhi Bose Recently, multiple convection-roll states were identified in two-dimensional planar Rayleigh-Bénard convection (Wang et al. 2020, Phys. Rev. Lett., 125(7), 074501). Different convection-roll states in the initial condition yielded these multiple states in simulations. Herein, we propose a framework that intrusively suppresses select non-linear triad interactions to yield these multiple states irrespective of the initial state. The intrusive framework is based on the observation that convection-roll wavenumber mediates triadic scale interactions resulting in both kinetic and thermal energy cascades which are dominant energy transfer processes in statistically stationary roll states. Suppression of these cascades mediated by a candidate wavenumber hinders the formation of convection rolls at that wavenumber. As a consequence, another candidate wavenumber which is allowed to mediate energy to establish the cascade processes, forms the convection rolls. In case, no stable convection-roll states are possible, this technique does not yield any convection rolls making it a suitable method for discovery of multiple states. This forcing technique is able to yield accurate predictions of statistical quantities such as Nusselt number and volume-averaged Reynolds numbers. The convection-roll states yielded using this technique may be used as initial conditions for direct simulations quickly converging to the target roll state without taking long convergence routes involving state transitions. |
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C16.00018: An asymptotic theory for wall modes in rapidly-rotating Rayleigh-Benard convection Geoffrey Vasil, Daniel Lecoanet, Keaton J Burns, Benjamin P Brown, Jeffrey S Oishi, Keith A Julien At low Ekman number (Ek), the onset of convection is via wall modes: instabilities that are localized to the vertical boundaries. The wall modes lead to important heat transfer and fluid motions, even when the convection is sufficiently supercritical that both wall and bulk modes are present. While wall modes have been studied experimentally and via direct numerical simulations, neither approach can reach the low Ek of geophysical flows, e.g., convection in the Earth's outer core. Here we use multiple-scale asymptotic analysis to derive a set of integro-differential equations capturing the dynamics of wall modes in the Ek->0 limit. These equations match ``bulk'' variables, which satisfy geostrophic and thermal wind balance, to ``boundary layer'' variables which vary on a small length scale O(Ek^1/3) in the vertical side-wall thermal boundary layers. The boundary layer problem can be solved to leading order, yielding a non-linear and non-local boundary condition for the bulk variables. We solve these equations in cylindrical geometry using Dedalus for different reduced Rayleigh numbers R=Ra Ek, which asymptotically remains O(1). The numerical simulations match different qualitative and quantitative features observed in finite-Ek DNS and experiments, including front-like features which propagate around the cylinder at a characteristic velocity. Intriguingly, our simulations show this propagation velocity decreases with increasing R, even reversing direction for high supercriticality. |
Sunday, November 24, 2024 11:20AM - 12:50PM |
C16.00019: INTERACT DISCUSSION SESSION WITH POSTERS: Rotating and Non-Rotating Rayleigh-Benard Convection After each Flash Talk has concluded, the Interact session will be followed by interactive poster or e-poster presentations, with plenty of time for one-on-one and small group discussions. |
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C16.00020: Abstract Withdrawn |
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