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 G33: Free and Rayleigh-Benard Convection II |
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Chair: Olga Shishkina, Max Planck Institute Room: Georgia World Congress Center B405 |
Monday, November 19, 2018 10:35AM - 10:48AM |
G33.00001: Boundary layer theory for turbulent Rayleigh-Benard convection: Approximation of a self-organized turbulent wind Olga Shishkina, Emily S.C. Ching We have derived a system of the boundary layer equations for turbulent Rayleigh-Benard convection (RBC), where we consider a quasi-two-dimensional fluid flow along a semi-infinite horizontal heated plate with the requirement that the horizontal velocity vanishes far away from the plate. This boundary condition, which reflects the fact that the time-averaged horizontal component of the wind in RBC achieves its maximum value at a certain distance from the plate but vanishes in the core part of the cell, is different from what is considered in the Prandtl-Blasius or Falkner-Skan approximations. In this talk, we focus on the development of the velocity boundary layer equation. The turbulent fluctuations in the equation are taken into account by an eddy viscosity, which, based on Prandtl's mixing length ideas, is related to the dimensionless stream function. |
Monday, November 19, 2018 10:48AM - 11:01AM |
G33.00002: Directional change of tracer trajectories in rotating Rayleigh-Bénard convection Kim M.J. Alards, Hadi Rajaei, Rudie Kunnen, Federico Toschi, Herman Clercx In Lagrangian measurements of turbulence the complexity is reflected in the directional changes of tracer trajectories over many active timescales. We study angular statistics of tracer trajectories in rotating Rayleigh-Bénard convection both experimentally and numerically. Our aim is to explore the geometrical characterization of flow structures in turbulent convection in a wide range of timescales and how it is affected by background rotation. We find that the angle of directional change θ(τ) as a function of the time gap τ is distributed similarly as in homogeneous isotropic turbulence. The ensemble averaged angle Θ(τ) = 〈|θ(τ)|〉 displays a transition from a ballistic scaling Θ(τ) ∼ τ for τ < τ_{η }(the Kolmogorov timescale), to an inertial-range scaling Θ(τ) ∼ τ^{c} with smaller exponent c < 1 for τ_{η} < τ < T_{L} (the Lagrangian integral timescale). We show that the value of c is related with the dominant flow structures: the large-scale circulation for slow rotation and vertically aligned vortices emerging from the boundary layers for rapid rotation. |
Monday, November 19, 2018 11:01AM - 11:14AM |
G33.00003: Boundary layer theory for turbulent Rayleigh-Benard convection: Temperature boundary layer profiles Emily S.C. Ching, H.S. Leung, Olga Shishkina |
Monday, November 19, 2018 11:14AM - 11:27AM |
G33.00004: Abstract Withdrawn We present an experimental study of natural convective flows inside a cylindrical cavity with aspect ratio (height/diameter) 1.2. Water is the working fluid (Pr= 6.67) and the description of the flow is made in terms of the Rayleigh number. Velocity fields and Lagrangian orbits are obtained with time-resolved tomographic PIV and particle tracking techniques respectively. The observations contain information on the three component, volumetric velocity field in steady state (Ra < 10^{6}) and in time-dependent flows (Ra > 10^{6}). Detailed topological properties of the flows and orbits are reported for steady state including symmetries, critical lines and planes, geometrical properties of orbits and vortex cores. Experiments allow observing the transition from steady state to time-dependent flow as the Rayleigh number is increased. Also, the properties of the bifurcation and the time evolution of convective patterns can be studied with the information available. |
Monday, November 19, 2018 11:27AM - 11:40AM |
G33.00005: Using topology to identify large Lyapunov vector magnitude in Rayleigh-Bénard convection Brett Tregoning, Rachel Levanger, Jacek Cyranka, Saikat Mukherjee, Mark Richard Paul, Konstantin Mischaikow, Michael F Schatz Persistent homology is a tool from algebraic topology that can be used to efficiently detect pattern features in image data. In the spatio-temporally chaotic flow known as spiral defect chaos in Rayleigh-Bénard convection, we investigate how pattern features detected in laboratory experiments can be related to leading-order Lyapunov vectors computed from convection simulations. In particular, we demonstrate that convective plumes, detected using persistent homology, are strongly correlated to spatially-localized regions of high magnitude of leading-order Lyapunov vectors in simulations. Additionally, we show that plume statistics are similar for both patterns in experiments and in simulations at the same parameter values. These results suggest that plumes detected by persistent homology reliably indicate spatial locations in convection experiments that are sensitive to small disturbances. |
Monday, November 19, 2018 11:40AM - 11:53AM |
G33.00006: Signature of Optimal Coherent Structures in Turbulent 2D Rayleigh Benard Convection Parvathi Madathil Kooloth, Leslie Morgan Smith, David Sondak Steady solutions that maximize the heat transport in 2D Rayleigh Bénard convection (RBC) with no-slip horizontal walls have been studied in detail in Waleffe, Boonkasame & Smith (2015) and Sondak, Smith & Waleffe (2015). The close agreement of Nu-Ra scaling of the optimal solutions with data from 3D simulations and experiments suggests a link between the optimal coherent structures and turbulent 3D RBC. We explore this connection by searching for signatures of the optimal solutions in 2D turbulent RBC. Spatial correlations between the optimal structures and turbulent fields are computed at a variety of Pr and Ra in high aspect ratio domains. Our results show highly correlated (> 0.8) structures that resemble the optimal structure appear frequently throughout the turbulent flow field. The similarities in these structures are especially pronounced in the boundary layer. We compare momentum and thermal boundary layer scaling between the optimal and turbulent solutions and find that they are in very good agreement. As a precursor to stability analysis of the optimal solutions, the effect of mean flow on the agreement between statistics of the optimal and turbulent solutions is diagnosed using additional turbulent simulations that exclude mean flows by imposing mirror symmetry. |
Monday, November 19, 2018 11:53AM - 12:06PM |
G33.00007: Probing turbulent superstructures in Rayleigh-Bénard convection by Lagrangian trajectory clusters Joerg Schumacher, Christiane Schneide, Ambrish Pandey, Kathrin Padberg-Gehle We analyse the formation of large-scale patterns in a turbulent convection flow in a horizontally extended square convection cell by Lagrangian particle trajectories in three-dimensional direct numerical simulations. These large-scale patterns, which are termed turbulent superstructures of convection, are detected by the spectrum of the graph Laplacian matrix. The corresponding graph is built from the Lagrangian particle tracks. We demonstrate that the resulting trajectory clusters, which are obtained by a subsequent k-means clustering, agree with the superstructures in the Eulerian frame of reference. Furthermore, the characteristic times τ ^{L} and lengths λ_{U}^{L} of the superstructures are found to agree well with their Eulerian complements, τ and λ_{U}, respectively. The clustering works well for times t < τ. Longer times t > τ require density-based trajectory clustering using time-averaged Lagrangian pseudo-trajectories. A coherent subset of these trajectories is obtained which consists of those particles tracks that are trapped for long times in the core of the superstructure rolls and thus not subject to ongoing turbulent dispersion. |
Monday, November 19, 2018 12:06PM - 12:19PM |
G33.00008: Rotating Rayleigh–Bénard convection and non-Boussinesq effects in pressurized SF_{6} Xuan Zhang, Olga Shishkina Rotating Rayleigh–Bénard convection (RBC) in pressurized sulfur hexafluoride (SF_{6}) with Prandtl number Pr=0.8 is investigated numerically based on direct numerical simulations (DNS) using finite-volume code GOLDFISH. A cylindrical cell of aspect ratio 1/2 (diameter-to-height) is considered, and the parameters studied are Rayleigh number from 10^{8 }to 10^{10} and Rossby number Ro from 0.02 to 50. |
Monday, November 19, 2018 12:19PM - 12:32PM |
G33.00009: Bounding heat transport for a model of Rayleigh-Benard convection using sum-of-squares optimization Matthew Olson, David Goluskin, William W Schultz, Charles R Doering We determine bounds on the maximum rate of heat transport (Nusselt number) for an 8-ODE model of Rayleigh-Benard convection developed by Gluhovsky et al. (2002). This truncated model is distinguished in the sense that it obeys many desired conservation laws and physical properties of the PDE. We use a general framework for bounding infinite-time averages in dynamical systems, which is similar to the use of Lyapunov functions in stability theory. Applying this framework, the maximal heat transport problem is computed numerically using sum-of-squares optimization. New upper bounds are established for the truncated system that are sharper than previously known bounds derived by Souza and Doering (2015). Additionally, the numerical results are used to inform the construction of new analytical bounds for the truncated model. |
Monday, November 19, 2018 12:32PM - 12:45PM |
G33.00010: Superstructures in inclined thermal convection of low-Prandtl-number fluids Lukas Zwirner, Olga Shishkina Any tilt of a Rayleigh-Benard convection (RBC) cell against gravity changes the global flow structure inside the cell. Recent experiments by Vasil'ev et al., Tech. Phys. 60 (2015), and Frick et al., Europhys. Lett. 109 (2015), with liquid sodium (Prandtl number Pr=0.0089) demonstrated that the heat transport in low-Pr fluids and for small diameter-to-height aspect ratio containers is especially sensitive to the inclination angle. Our study of inclined convection in a cylindrical container of the aspect ratio 1/5 is based on direct numerical simulations (DNS) and we consider Pr≤1. We demonstrate that flow superstructures like the large scale circulation and boundary layers (BLs) are influenced by both, the inclination angle and the lateral confinement. For inclined convection we observe the formation of two system-sized plume columns, a hot and a cold one, that impinge on the opposite BLs, see Zwirner and Shishkina, J. Fluid Mech. 850 (2018). In RBC the confined cell supports the formation of multiple rolls on top of each other. |
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