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 R16: Convection and Buoyancy-Driven Flows: General III |
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Chair: Ross Griffiths, Australian National University Room: 2000 |
Tuesday, November 25, 2014 1:05PM - 1:18PM |
R16.00001: Statistical description of the main modes of Rayleigh-Benard convection Johannes Luelff Rayleigh-Benard convection, which is the buoyancy-induced movement of a fluid enclosed between two horizontal plates, is an idealized setup to study thermal convection. The temperature fluctuations of the fully turbulent case are of special interest, which we are investigating by a statistical description coupled with a mode projection ansatz. To this end, we characterize the statistics of temperature fluctuations by investigating the probability density function (PDF) of temperature with the help of DNS data. This gives us insights into the mean dynamics of the convecting fluid. We then apply a projection of the data onto the main modes by using the POD ansatz. Thereby, we can determine the modes with the major influence on the mean dynamics and the coherent structures in the convection cell. [Preview Abstract] |
Tuesday, November 25, 2014 1:18PM - 1:31PM |
R16.00002: Using Persistent Homology to Describe Kolmogorov Flow and Rayleigh-B\'enard Convection Jeffrey Tithof, Balachandra Suri, Samuel Raben, Miroslav Kramar, Rachel Levanger, Mu Xu, Mark Paul, Konstantin Mischaikow, Michael Schatz We employ a new technique for describing the dynamics of spatially extended systems evolving in time. In particular, we study two canonical fluid flows: Kolmogorov flow and Rayleigh-B\'enard convection. The technique used, known as persistent homology, provides a powerful mathematical tool in which the instantaneous topological characteristics of the system are encoded in a so-called persistence diagram, which is independent of the global symmetries of the system. By applying a metric to measure the distances across multiple persistence diagrams, we can quantify the symmetry-independent similarities between states, providing an opportunity for unique physical insights into the time evolution of a dynamical system. The two systems studied are particularly interesting, as each display a wide range of dynamical behavior and possess their own symmetries. We perform our analysis using flow field patterns from numerical simulations of these systems; however, we emphasize that our analysis can be conducted with patterns measured in experiment. Our results show that persistent homology is a powerful way to gain new physical insights into the complex dynamics of large spatially extended systems that are driven far-from-equilibrium. [Preview Abstract] |
Tuesday, November 25, 2014 1:31PM - 1:44PM |
R16.00003: ABSTRACT WITHDRAWN |
Tuesday, November 25, 2014 1:44PM - 1:57PM |
R16.00004: Inhomogeneous temperature boundary conditions in Rayleigh-B\'enarrd convection Roberto Verzicco, Dennis Bakhuis, Rodolfo Ostilla-Monico, Erwin van der Poel, Detlef Lohse In the ideal Rayleigh-B\'enard problem it is assumed that the fluid layer is heated and cooled, respectively from below and above, by isothermal surfaces that strictly maintain the temperature constant regardless of the flow dynamics. This is however only an approximation since all thermal sources have properties that couple with those of the fluid. In this study we analyze, by three-dimensional direct numerical simulations, the heat and flow dynamics when the plates have non homogeneous temperature boundary conditions in order to understand to what degree the Nusselt number is affected. Several ``temperature patterns'' have been imposed on the plates with the Nusselt number that has shown a surprising robutness to the temperature inhomogeneity. The investigation is further extended to cases in which the plates are made by a sandwich of different materials and the temperature is inhomogeneous also within the plate thickness. [Preview Abstract] |
Tuesday, November 25, 2014 1:57PM - 2:10PM |
R16.00005: A Comparative Experimental Study of Fixed Temperature and Fixed Heat Flux Boundary Conditions in Turbulent Thermal Convection Shi-Di Huang, Fei Wang, Heng-Dong Xi, Ke-Qing Xia We report an experimental study of the influences of thermal boundary condition in turbulent thermal convection. Two configurations were examined: one was fixed heat flux at the bottom boundary and fixed temperature at the top (HC cells); the other was fixed temperature at both boundaries (CC cells). It is found that the flow strength in the CC cells is on average 9{\%} larger than that in the HC ones, which could be understood as change in plume emission ability under different boundary conditions. It is further found, rather surprisingly, that flow reversals of the large-scale circulation occur more frequently in the CC cell, despite a stronger large-scale flow and more uniform temperature distribution over the boundaries. These findings provide new insights into turbulent thermal convection and should stimulate further studies, especially experimental ones. [Preview Abstract] |
Tuesday, November 25, 2014 2:10PM - 2:23PM |
R16.00006: Simulating Wall-Mode Convection: Numerical Techniques and First Results Keaton Burns, Geoffrey Vasil We present simulations of strongly nonlinear wall-mode convection in rapidly rotating containers. Using an asymptotically reduced model developed by G.~Vasil \& K.~Julien, we examine the instability and subsequent pattern formation of a confined rotating system heated from below, in a regime where the system is stable against bulk convection but strongly unstable to precessing modes localized to the container sidewalls. The model includes nonlinear and nonlocal boundary conditions which feedback onto the interior dynamics, and separate prognostic equations governing the barotropic and baroclinic components of the flow. We implement these equations in channel and cylindrical geometries using Dedalus, a new open-source pseudospectral code. [Preview Abstract] |
Tuesday, November 25, 2014 2:23PM - 2:36PM |
R16.00007: Buoyancy-induced turbulent mixing in a narrow tilted tank Tiras Y. Lin, C.P. Caulfield, Andrew W. Woods We describe a series of experiments in which a constant buoyancy flux $B_s$ of dyed salty water of density $\rho_s$ is introduced at the top of a long narrow tank of square cross-section tilted at an angle $\theta$ from the vertical. The tank is initially filled with fresh clear water of density $\rho_0<\rho_s$, and we investigate the resulting buoyancy-driven high Reynolds number turbulent mixing at various tilt angles $\theta$ using a light-attenuation method. When $\theta>0^{\circ}$, the ensemble averaged reduced gravity develops a statically stable gradient normal to the walls of the tank, and this induces a counterflow. We model the evolution of the cross-tank and ensemble averaged reduced gravity $\left<\overline{g'}\right>_e$ as a diffusive process using Prandtl's mixing length theory, building on the model of van Sommeren \textit{et al.} (\textit{JFM} \textbf{701}, 2012) who considered vertical tanks. We show that the counterflow acts to enhance the effective along-tank turbulent diffusivity, and from experiments, we find that the mixing length increases approximately linearly with $\theta$, and that both the along-tank and cross-tank turbulent diffusivities are proportional to $\left(\partial\left<\overline{g'}\right>_e/\partial z \right)^{1/2}$. [Preview Abstract] |
Tuesday, November 25, 2014 2:36PM - 2:49PM |
R16.00008: Turbulent thermal convection in two superposed fluid layers Yi-Chao Xie, Ke-Qing Xia We present an experimental investigation of turbulent thermal convection in a cylindrical cell with two superposed immiscible fluid layers, namely water layer above fluorinert FC-77 electronic liquid (FC77) layer. The flow dynamics and coupling are studied using a multi-thermal-probe method. It is found that while one large-scale circulation (LSC) still exists in each fluid layer, their dynamics change dramatically compared to the single-layer case. Cessations of the LSC in FC77 of the two-layer system occur much more frequently than they do in single layer case and a cessation is most likely to result in a reversal, which can be understood as a symmetry breaking imposed be the orientation of the LSC in the water layer that remained unchanged most of the time. It is further found that the frequently occurring cessations and reversals are caused by the system switching between its two metastable state, i.e. thermal and viscous coupling modes with the former as the predominant one. It is also observed that the influence of the LSC in one fluid layer on the other is not symmetric, i.e. the strength of the LSC in water becomes weaker when the LSC in FC77 rotates faster azimuthally and that the flow strength in FC77 becomes stronger when the LSC in water rotates faster azimuthally. [Preview Abstract] |
Tuesday, November 25, 2014 2:49PM - 3:02PM |
R16.00009: Turbulent convection from a 2D array of heating and cooling Ross Griffiths, Bishakhdatta Gayen Recent simulations of Rayleigh-B\'enard convective turbulence showed that an asymptotic state is attained at $Ra>>10^{10}$, where flow is dominated by long-lived, large-scale structures that, in turn, undergo shear instability leading to production of the small scales of turbulence and viscous dissipation at a rate similar to turbulent mixing. Here we show that neither a net heat input nor a global temperature gradient is required to produce turbulence. Convection is simulated above a horizontal plate having a 2D sinusoidal array of many warm and cold patches with the system allowed to evolve to the thermal equilibrium state in which there is no net heat flux through the boundary. This is ``horizontal convection,'' but replacing the usual 1D distribution of boundary temperature and domain scale of forcing to allow full three-dimensionality for all scales of flow and a forcing scale much smaller than the domain. DNS reveals a full spectrum of scales dominated, for a deep domain, by the emergence of box-scale structures much larger than the scale of the forcing. In this flow the Reynolds number is large despite small viscous dissipation, demonstrating that zero net buoyancy flux does not constrain the amount of kinetic energy in a flow dominated by turbulent mixing and diffusion. [Preview Abstract] |
Tuesday, November 25, 2014 3:02PM - 3:15PM |
R16.00010: The Continental Drift Convection Cell John Whitehead, Mark Behn Continents on Earth periodically assemble to form supercontinents, and then break up again into smaller continental blocks (the Wilson Cycle). Highly developed, realistic numerical models cannot resolve if continents respond passively to mantle convection or whether they modulate flow. Our simplified numerical model addresses this: A thermally insulating continent floats on a stress-free surface for infinite Prandtl number cellular convection with constant material properties in a chamber 8 times longer than depth. The continent moves back and forth across the chamber driven by a ``continental drift convection cell'' of a form not previously described. Subduction exists at the upstream end with cold slabs dipping at an angle beneath the moving continent. Many continent/subduction regions on Earth have this feature. Drift enhances vertical heat transport by approximately 30{\%} compared to a fixed continent, especially at the core-mantle boundary. Drift also significantly decreases lateral mantle temperature differences but it has smaller effects on profiles of horizontally averaged temperature. Although calculations are done at Rayleigh numbers lower than expected for Earth's mantle (2x10$^{\mathrm{5}}$ and 10$^{\mathrm{6}})$, the drift speed extrapolates to reasonable Wilson Cycle speeds for larger \textit{Ra}. [Preview Abstract] |
Tuesday, November 25, 2014 3:15PM - 3:28PM |
R16.00011: Salinity transfer in double diffusive convection bounded by two parallel plates Yantao Yang, Erwin P. van der Poel, Rodolfo Ostilla-Monico, Chao Sun, Roberto Verzicco, Siegfried Grossmann, Detlef Lohse The double diffusive convection (DDC) is the convection flow with the fluid density affected by two different components. In this study we numerically investigate DDC between two parallel plates with no-slip boundary conditions. The top plate has higher salinity and temperature than the lower one. Thus the flow is driven by the salinity difference and stabilised by the temperature difference. Our simulations are compared with the experiments by Hage and Tilgner (\emph{Phys. Fluids}, vol.~22, 076603, 2010) for several sets of parameters. Reasonable agreement is achieved for the salinity flux and its dependence on the salinity Rayleigh number. For all parameters considered, salt fingers emerge and extend through the entire domain height. The thermal Rayleigh number shows minor influence on the salinity flux although it does affect the Reynolds number. We apply the Grossmann-Lohse theory for Rayleigh-B\'{e}nard flow to the current problem without introducing any new coefficients. The theory successfully predicts the salinity flux with respect to the scaling for both the numerical and experimental results. [Preview Abstract] |
Tuesday, November 25, 2014 3:28PM - 3:41PM |
R16.00012: Spatially localized convection in a rotating layer Edgar Knobloch, Cedric Beaume, Alain Bergeon, Hsien-Ching Kao We study two-dimensional stationary convection in a horizontal fluid layer heated from below and rotating about the vertical. With stress-free boundary conditions at top and bottom, spatially localized states can be found that are embedded in a self-generated background shear zone and lie on a pair of intertwined solution branches exhibiting ``slanted snaking.'' States of this type are present even in the absence of bistability between conduction and periodic convection -- a consequence of the conservation of zonal momentum.\footnote{C. Beaume et al., J. Fluid Mech. 717, 417 (2013)} With no-slip boundary conditions this quantity is no longer conserved but localized states continue to exist. These are no longer embedded in a background shear zone and exhibit standard snaking. Homotopic continuation from free-slip to no-slip boundary conditions is used to track the changes in the properties of the solutions and the associated bifurcation diagrams.\footnote{C. Beaume et al., Phys. Fluids 25, 124105 (2013)} [Preview Abstract] |
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