Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session E33: Turbulent Convection I |
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Chair: Jared Whitehead, Brigham Young University Room: Georgia World Congress Center B405 |
Sunday, November 18, 2018 5:10PM - 5:23PM |
E33.00001: Bounds on heat transport in rotating Rayleigh-Bénard convection Jared Whitehead Traditional methods providing bounds on the heat transport in convective flows do not account for the influence of rigid body rotation, as these methods typically rely on energy type estimates. We demonstrate these difficulties and show several approaches that do yield insight into the effects of rigid body rotation on the convective heat transport. Most of these bounds are determined first via numerical solution of semi-definite programs, providing insight into rigorous upper bounds via the auxiliary functional method. |
Sunday, November 18, 2018 5:23PM - 5:36PM |
E33.00002: Centrifugal-buoyancy-driven vortex motion and symmetry breaking in rotating Rayleigh-Bénard convection Shan-Shan Ding, Hao-Yuan Lu, Jun-Qiang Shi, Jin-Qiang Zhong We report measurements of the horizontal motion of columnar vortices in rapidly rotating Rayleigh-Bénard convection at a fluid height z=H/4 of a cylindrical cell. With the Froude number Fr<0.05, the vortices are advected laterally in a random manner that reveals the character of Brownian motion. When Fr>0.05, the centrifugal buoyancy starts to influence the vortical dynamics, leading to prominent radial vortex motions: uprising (hotter) cyclones are attracted towards the rotating axis while downwelling (cooler) anticyclones are accelerated outwards. The ensemble statistics of the vortex trajectories is interpreted by a set of Langevin equations which incorporates a parabolic potential associated with the centrifugal force. Strong centrifugal buoyancy creates a noticeable radial thermal gradient in the background fluid with warmer fluid accumulated near the cell center. For a certain parameter range this effect breaks the symmetry of the vorticity in the sense that anticyclones become stronger than cyclones in the inner region. In consequence we observe abnormal cyclonic motion when both cyclones and anticyclones are moving outwards as they form clusters of regular vortex grid. |
Sunday, November 18, 2018 5:36PM - 5:49PM |
E33.00003: From gradual to sharp transitions, heat transport in rapidly rotating Rayleigh-Bénard Convection Jin-Qiang Zhong, Jun-Qiang Shi, Hao-Yuan Lu We present experimental measurements of the heat transport in rapidly rotating Rayleigh-Bénard convection for cylindrical samples of water (Pr=4.38) with diameter D=24.0cm and various aspect ratios of 0.4≤Γ≤4.0. Results for the Nu as a function of Ra reveal a gradual transition from weakly rotating convection to rotation-dominated geostrophic convection in a low-Ra regime Ra≤5.0*107. However, in a high-Ra regime with Ra≥1.0*109, a sequence of sharp transitions appears in Nu(Ra) when Ra is increased. With Γ=0.4 data of Nu(Ra) in the geostrophic turbulence regime (Ek≤10-6 and Ra≥3Rac with Rac=8.7*Ek-4/3) suggest a universal scaling relationship Nu=(Ra/Rac)1.4 independent on the Ek number. |
Sunday, November 18, 2018 5:49PM - 6:02PM |
E33.00004: Sharp transitions in the Lagrangian acceleration statistics in rotating Rayleigh-Benard convection Kim M.J. Alards, Rudie Kunnen, Richard Stevens, Detlef Lohse, Federico Toschi, Herman Clercx Rotation induces transitions in the heat transfer and flow structures in Rayleigh-Benard convection. While the transition in the heat transfer is definitely sharp, it is not clear whether the transition in the flow structures reveals a similar sharpness. We investigate this transition by studying Lagrangian acceleration statistics of passive tracers. Near the top plate, the intermittency of the acceleration statistics suddenly increases at a critical Rossby number, Roc = 2.25. To understand this sudden increase, we focus on the relation between the acceleration and the dynamics of plumes developing in the boundary layers, which are typically characterized by large values of vorticity. When Ro>2.25 no correlation is found between the extreme acceleration events and vertical vorticity. For Ro<Roc the values of (positive) vertical vorticity have increased significantly and now extreme acceleration events are correlated to large vorticity. This suggests that the sharp transition in the Lagrangian acceleration statistics is related to vortical plumes developing in the Ekman boundary layer for Ro<Roc. |
Sunday, November 18, 2018 6:02PM - 6:15PM |
E33.00005: Fine structures of the convective Taylor columns in rotating Rayleigh-Bénard convection Jun-Qiang Shi, Hao-Yuan Lu, Shan-Shan Ding, Jin-Qiang Zhong Under strong rotations, the flow structure in turbulent Rayleigh-Bénard convection is mainly manifested as convective Taylor columns (CTC) traversing the upper and lower boundary layers. We present high-resolution PIV measurements of the fine structures of the CTC in a cylindrical sample over the range of Rayleigh number 2.0×107≤Ra≤8.2×109, Taylor number 5.5×107≤Ta≤7.5×1011 and Prandtl number Pr=4.38. Results of the velocity fields in a horizontal plane show that the azimuthal velocity within the CTC has a universal radial profile VΦ(r/r0) with varying vortex radius r0. Velocity data in vertical planes passing through the vortex centers suggest that the radial dependence of the vertical velocity is dictated by Hankel functions in agreement with pervious theoretical predictions. Our velocity-field data further reveal the vortical-sheath structure surrounding the CTC with its strength dependening on Ta. |
Sunday, November 18, 2018 6:15PM - 6:28PM |
E33.00006: Effects of fluid properties on sheared thermal convection Alexander Blass, Xiaojue Zhu, Pier Tabak, Roberto Verzicco, Detlef Lohse, Richard Stevens A series of direct numerical simulations of sheared thermal convection have been performed with a second-order finite difference code (van der Poel et al., Comp. & Fluids, 116:10-16, 2015), optimized for a GPU cluster (AFiD GPU (Zhu et al., Comp. Phys. Comm., 229:199-210, 2018)), with a Rayleigh number Ra = 1x106 and a wall Reynolds number Rew of 0 ≤ Rew ≤ 4000. We study the Prandtl number (Pr) dependency of flow structures in the regime of 0.22 ≤ Pr ≤ 4.6. Our findings show that a high Pr results in an increased dependency of Nusselt number and Rew. At Pr = 4.6 we find a dependency of Nu(Rew) ∝ 1x10-3 Rew in the shear dominated regime, while in the same regime for Pr = 0.22 and Pr = 0.46, Nu(Rew) seems to collapse at Nu(Rew) ∝ 1x10-4 Rew. Additionally, we study the bulk Richardson number Rib - the ratio of buoyancy to mechanical forcing. For low Rib the flow settles in a regime dominated by the flow shearing, while a thermally dominated regime is present for high Rib. Various flow statistics have been plotted as a function of Rib-1 to determine whether the Richardson number is a good estimator of the flow behavior. We show that in the studied parameter space Rib-1 Ra0.31 predicts Nu within 10%. |
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