Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session G19: Convection and Buoyancy-Driven Flows: Rotation |
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Chair: Jin-Qiang Zhong, Tongji University Room: 2006 |
Monday, November 24, 2014 8:00AM - 8:13AM |
G19.00001: Influence of the Prandtl number on the heat transport enhancement in rotating turbulent Rayleigh-B\'enard convection Stephan Weiss, Ping Wei, Guenter Ahlers We present new Nusselt-number (Nu) measurements for slowly rotating turbulent thermal convection in cylinders with aspect ratio $\Gamma=1$. By using compressed gasses and various liquids, we now have data in the Prandtl number (Pr) range $0.74<$Pr$<35.5$ and for Rayleigh numbers (Ra) in the range $4\times 10^8<$Ra$<2\times 10^{11}$. With these data we investigate in detail the effect of Pr and Ra on the heat-transport enhancement close to its onset. This enhancement takes place for rotation rates larger than a critical value, as expressed by the dimensionless inverse Rossby number ($1/Ro$), since only then vortices form, in which due to Ekman pumping fluid is transported from the thermal boundary layers into the turbulent bulk. We found that the critical inverse Rossby number ($1/Ro_c$) decreases with increasing Pr, following a power law with exponent $\alpha=-0.40 \pm0.02$. For larger rotation rates, the relative heat transport enhancement ($Nu_r$) increases first linearly with a slope $S=\partial Nu_r/\partial(1/Ro)$. We show that also the slope $S$ follows a power law $S\propto Pr^\beta Ra^\gamma$ with $\beta=-0.10 \pm 0.06$ and $\gamma=-0.14 \pm 0.04$. We found that the maximum heat transport enhancement (up to 40\% ) increases with increasing Pr and decreasing Ra. [Preview Abstract] |
Monday, November 24, 2014 8:13AM - 8:26AM |
G19.00002: Dynamics of the large-scale circulation in turbulent Rayleigh-B\'enard convection with modulated rotation Jin-Qiang Zhong, Sebastian Sterl, Hui-Min Li We present measurements of the azimuthal rotation velocity $\dot{\theta}$ and thermal amplitude $\delta$ of the large-scale circulation (LSC) in turbulent Rayleigh-B\'enard convection with modulated rotation. Both $\dot{\theta}$ and $\delta$ exhibit clear oscillations at the modulation frequency $\omega$. Fluid acceleration driven by oscillating Coriolis force plays a role in determining the LSC rotations and causes an increasing phase lag in $\dot{\theta}$ when $\omega$ increases. The applied modulation also produces oscillatory boundary layers and the resulting time-varying viscous drag modifies $\delta$ periodically. Oscillation of $\dot{\theta}$ with the maximum amplitude occurs at an intermediate ${\omega}^{\star}$. Such a resonance-like phenomena is interpreted as a result of the optimal coupling of $\delta$ to the sample rotation velocity. We show that an extended LSC model with a relaxation time for $\delta$ to response to modulated rotations provides predictions in close agreement with the experimental results. [Preview Abstract] |
Monday, November 24, 2014 8:26AM - 8:39AM |
G19.00003: Retrograde rotation of the large-scale circulation in turbulent rotating Rayleigh-Benard convection at large Rossby numbers up to 200 Hui-Min Li, Jin-Qiang Zhong We examine the azimuthal rotation of the large-scale circulation (LSC) for turbulent Rayleigh-Benard convection in the present of week rotations about a vertical axis at angular velocities $1.0{\times}10^{-3}{\le}{\Omega}{\le}0.1$(rad/s). Over the entire Rossby-number range $1{\le}Ro{\le}200$ studied, linear retrograde rotations of the LSC circulating plane are observed. With increasing $Ro({\sim}{1/\Omega})$ the retrograde rotating velocity ${\langle}-\dot{\theta}{\rangle}$ decreases monotonically, but the ratio ${\gamma}={\langle}-\dot{\theta}{\rangle}/{\Omega}$ experiences a transition at $Ro^{\star}{\approx}80$ above which ${\gamma}$ increases sharply. We discuss the $Ro$-dependence of ${\gamma}$ for $Ro>Ro^{\star}$ and show that a maximum ratio ${\gamma_{max}}=0.36$ is observed at $Ro=200$, more than twice larger than other results reported before in a lower-Ro regime [1]. The experimental findings may shed new light to interpret the low precession rate under weak Coriolis force within the framework of the LSC models [2].\\[4pt] [1] J. E. Hart, S. Kittelman, and D. R. Ohlsen, Phys. Fluids 14, 955 (2002); J.-Q. Zhong and G. Ahlers, J. Fluid. Mech. 665, 300 (2010).\\[0pt] [2] E. Brown and G. Ahlers, Phys. Fluids 18, 125108 (2006). [Preview Abstract] |
Monday, November 24, 2014 8:39AM - 8:52AM |
G19.00004: Lagrangian analysis of turbulent rotating convection Hadi Rajaei, Rudie Kunnen, Herman Clercx This study focuses on exploring how the flow transition from one state to the other in rotating convection will affect the Lagrangian statistics of (fluid) particles. Up to now, the global parameters like the overall heat transfer or the wind Reynolds number are used to characterize the different turbulent states. However, it is obvious that the flow transition from weakly rotating Rayleigh-Benard (RB) to strongly rotating RB is also reflected in the Lagrangian dynamics of immersed tracer particles. We have employed 3D Particle Tracking Velocimetry (3D-PTV) in a water-filled cylindrical tank of equal height and diameter 200 mm. The measurements are performed in the central volume of 50 x 50 x 50 mm$^3$ at a Rayleigh number Ra $=$ 1.28e9 and Prandtl number Pr $=$ 6.7. We are reporting the velocity and acceleration pdfs for different Rossby numbers and how transition from weakly rotating RB to strongly rotating RB affects the acceleration and velocity pdfs. [Preview Abstract] |
Monday, November 24, 2014 8:52AM - 9:05AM |
G19.00005: Cell pattern transitions on a rotating convection induced by internal heat generation Yuji Tasaka, Yudai Yamaguchi, Takatoshi Yanagisawa, Yoshihiko Oishi, Yuichi Murai We examined cell pattern formation on a rotating convection induced by internal heating. In this configuration with thermal insulation for the bottom boundary the thermal boundary layer whose separation provides convective motion exists only on the top boundary and the mechanism of the cell patter formation would be simpler than RBC. Flake visualization of the flow pattern indicated that there are three cell patterns on the marginal condition; irregular polygonal cells usually observed in internal heating convection, regular hexagonal cells, and time-dependent state as the results of competition of these patterns. These cell patterns are arranged by Rossby number. In the regular hexagonal cell pattern the fluid layer is occupied by regular hexagons like the rotating lattice observed in rotating RBC (Bajaj {\it et al}., 1998). But the cells do not show the continuous rotation unlike the rotating lattice but recreation of cells occurs intermittently in time and space. In a moderate condition, advecting local structures accompanied by sheet-like downward flows is observed instead of regular cell structures. This pattern is observed in a relatively large $Ta$ region and interruption of natural separation of the thermal boundary layer by thinning Ekman layer is an important factor. [Preview Abstract] |
Monday, November 24, 2014 9:05AM - 9:18AM |
G19.00006: Effect of rotation on the temperature profile of turbulent convection with a Prandtl number $Pr = 12.3$ Ping Wei, Guenter Ahlers We report on the influence of rotation about a vertical axis on the temperature profiles and the large-scale circulations (LSC) of turbulent Rayleigh-B\'enard convection (RBC) in a cylindrical sample with aspect ratio $\Gamma = D/L = 1.00$ (D is the diameter and L the height). The working fluid was a fluorocarbon at a mean temperature $T_{m} = 25^{\circ}$C with a Prandtl number $Pr = 12.3$. The measurements covered the Rayleigh-number range $2\times 10^{10} \leq Ra \leq 2\times10^{11}$ and the inverse Rossby number range $0\leq 1/Ro \leq 9$. With weak rotation the temperature in the fluid varied as $A\times ln(z/L) + B$, where z is the distance from the bottom or top plate. For $1/Ro \geq 1.2$ we found that the temperature varied linearly with z. The temperature signature of the LSC along the sidewall was detectable up to $1/Ro \simeq 0.5$. Retrograde rotation of the LSC was observed. The LSC temperature amplitude first decreased and then remained constant up to the critical inverse Rossby number $1/Ro_c$ for the onset of Ekman-vortex formation, and then decreased again. [Preview Abstract] |
Monday, November 24, 2014 9:18AM - 9:31AM |
G19.00007: Structure and local heat transport in the geostrophic regime of rotating Rayleigh-Benard convection Sergiy Gerashchenko, Scott Backhaus, Robert Ecke We report experimental measurements of velocity fields and local temperature for rotating thermal convection in the geostrophic range with Rayleigh number $10^7 < Ra < 2 \times 10^8$ and Taylor number $10^9 < Ta < 10^{10}$ (Ekman number $10^{-5} < Ek < 3 \times 10^{-5}$). The fluid is water with Prandtl number $Pr \approx 6$. The velocity was obtained in a 2 cm $\times$ 2 cm area using particle tracking velocimetry, and the temperature in the middle of that area was measured using a thermistor. The simultaneous velocity and temperature data allow the local heat transport to be obtained. We also compute the vertical and lateral spatial correlation lengths, the probability distribution functions of temperature and velocity, and the spatial structure of the velocity field of localized convective structures - thermal plumes for the non-rotating system and Taylor columns for convection with rotation. We present the dependence of these quantities for differing balances of buoyancy and rotation with Rossby number $Ro = \sqrt{Ra/Pr Ta}$ in the range $0.01 < Ro < 0.2$ and provide a characterization of the state of geostrophic rotating thermal convection for the regime with $Ra/Ra_c < 10$ where $Ra_c = 8.7 Ta^{4/3}$. [Preview Abstract] |
Monday, November 24, 2014 9:31AM - 9:44AM |
G19.00008: Natural Convection in a rotating multilayer spherical shell system with self gravity: A simplified global circulation model Francisco Javier Lira Rangel, Ruben Avila Rodriguez, Ares Cabello The onset of thermal convection in rotating multilayer spherical shells is investigated. The system consist of six concentric shells. The first spherical gap has an aspect ratio equal to 0.35, the following four spherical gaps have different aspect ratio and the sixth gap has an aspect ratio equal to 0.8. The inner and the outer spherical gaps confine Boussinesq fluids while the middle spherical gaps are treated as a thermal conductor solid. The investigation is performed for Taylor numbers between 7.E4 and 1.E6 and Rayleigh numbers between 3.E3 and 1.E6. The convective patterns and the temperature fields are presented in the most inner and outer spherical gaps. Convection is driven by the temperature difference between the inner and outer spheres and a gravitational field wich varies like $ r $ and $ 1/r^2 $. The fluid equations are solved by using the spectral element method (SEM). The mesh is generated by using the cubed-sphere algorithm to avoid the singularity at the poles. To the knowledge of the autors the convection-conduction-convection problem presented in this paper has not been investigated previously. [Preview Abstract] |
Monday, November 24, 2014 9:44AM - 9:57AM |
G19.00009: Thermal convection in a rotating fluid sphere with self gravity, uniform heat source and precession Ruben Avila The natural convection of a rotating fluid sphere with a self gravity field (which is proportional to the radius of the sphere) and with precessional motion is presented. The spherical bounding surface is maintained at a constant and uniform temperature which is lower than the temperature of the fluid. A constant and uniform heat source increases the temperature of the fluid confined in the sphere. The fluid sphere rotates and precesses with angular velocity vectors that form a certain inclination angle between them. The governing non-steady, three dimensional Navier-Stokes equations for an incompressible fluid, formulated in a Cartesian coordinate system (in the mantle reference frame) are solved by using the spectral element method. The influence of the Rayleigh number, the Ekman number and the Poincare number on the flow patterns, the temperature field and the heat transfer rate from the fluid sphere is presented. [Preview Abstract] |
Monday, November 24, 2014 9:57AM - 10:10AM |
G19.00010: A laboratory study of floating lenticular anticyclones Patrice Le Gal, Hector De La Rosa, Anne Cros, Ra\'ul Cruz-Gomez, Michael Le Bars Oceanic vortices play an important role in the redistribution of heat, salt and momentum in the oceans. Among these vortices, floating lenses or rings are often met in the meanders of warm currents. For instance the North Brazil Current rings are among the most intense and large anticyclonic vortices on Earth. In order to better describe these vortices, we propose here a laboratory study of these floating anticyclonic lenses. A blob of fresh water is slowly injected near the surface of a rotating layer of homogeneous salted water. Because of the opposite effects of rotation that tends to generate columnar structures and density stratification that spreads light water on the surface, the vortices take a finite size three dimensionnal typical shape. Visualization and PIV measurements of the shape, aspect ratios and vorticity profiles are compared to analytical predictions that use first a simple solid body rotation model and then a more realistic isolated Gaussian vorticity field inside the anticyclones. [Preview Abstract] |
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