Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session R2: Convection and Buoyancy-Driven Flows VIII |
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Chair: Ralf Wittenberg, Simon Fraser University Room: 23A |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R2.00001: Spatial localization due to the interaction between convection and a large scale mode Hsien-Ching Kao, Edgar Knobloch Spatially modulated states are of considerable interest in both rotating convection [1] and in magnetoconvection [2]. The formation of such states is due to the interaction between convective rolls and a large scale phase-like mode [3]: zonal velocity in rotating convection and magnetic potential in magnetoconvection. We have developed a higher order theory to describe the effects of spatial modulation near a certain codimension-two point where the leading order theory breaks down [1]. The theory leads to a fifth order Ginzburg-Landau equation with nonlocal terms. The properties of this equation are analyzed and the solutions used to explain the properties of spatially localized convectons in the full system determined numerically in [1,2].\\[4pt] [1] C. Beaume et al., submitted to J. Fluid Mech. (2012)\\[0pt] [2] D. Lo Jacono, A. Bergeon and E. Knobloch, J. Fluid Mech. 687, 595 (2011)\\[0pt] [3] S. M. Cox and P. C. Matthews, Physica D 149, 210229 (2001) [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R2.00002: Conservative bounds on heat transport in turbulent convection Ralf Wittenberg, Jared Whitehead The scaling dependence of the Nusselt number measuring heat transport in turbulent convection with the driving force remains incompletely understood, despite considerable effort in experiment, direct numerical simulation and theory. Variational upper bounds derived systematically from the governing partial differential equations provide a constraint on the possible scaling behaviors. We survey conservative analytical bounds on turbulent heat transport derived via the background flow method, both those obtained rigorously and semi-optimal upper bounds computed by numerical solution of the variational problem over a restricted class of backgrounds. We consider a range of scenarios, including the effects of plate conductivity, velocity boundary conditions and/or infinite Prandtl number in Rayleigh-B\'enard convection, as well as related problems such as internal-heating-driven and porous medium convection. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R2.00003: Localized structures in two-dimensional rotating convection Cedric Beaume, Alain Bergeon, Hsien-Ching Kao, Edgar Knobloch Geophysical flows exhibit localized structures such as cyclonic and anticyclonic vortices. We consider here convection in a two-dimensional fluid layer with stress-free fixed temperature boundaries rotating uniformly about the vertical [1], and focus on steady spatially localized structures called convectons. These solutions are of two types, odd and even parity, and are found in both subcritical and supercritical regimes [2]. We describe the properties of these convectons and use numerical continuation in a periodic domain to show that the convecton branches exhibit behavior known as slanted snaking. The results are compared to weakly nonlinear theory [2,3]. \\[4pt] [1] G. Veronis, J. Fluid Mech. 5, 401435 (1959)\\[0pt] [2] C. Beaume et al., preprint submitted to J. Fluid Mech. (2012)\\[0pt] [3] S. M. Cox and P. C. Matthews, Physica D 149, 210229 (2001) [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R2.00004: Pattern formation in nonlinear solutal Marangoni convection: three-dimensional simulations vs. experiments Thomas Koellner, Karin Schwarzenberger, Kerstin Eckert, Thomas Boeck We present simulations and related experiments of the stationary solutal Marangoni convection. We performed three dimensional DNS of a 2-layer fluid-fluid system with surfactant transfer from one layer to the other. Our simulations successfully reproduced the diverse set of flow patterns, which was so far only observed in the experiments. The highly resolved simulations are performed with a specialized spectral method. The experimental system is modeled by two immiscible Newtonian fluids. Both fluids are separated by a plane interface. Initially, a surface active agent(surfactant) is dissolved in the upper phase. The purely diffusive transport of the surfactant is unstable to the stationary Marangoni instability due to variations of the interfacial solute concentration. The surfactant transport at the interface is modeled by Henry's law. The Schmidt number for the considered organic surfactant is usually much more than a thousand. The dynamics of the evolving patterns are described in detail and compared to experimental observation for a cyclohexanol/water system with butanol as transported solute. We classify the emerging structures and analyze their characteristic length scales in terms of the velocity and surfactant distribution. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R2.00005: Weakly nonlinear stability of Marangoni convection in a liquid bridge Kaoru Fujimura Marangoni convection arising in a liquid column, bridging between concentric, circular parallel plates with different but uniform temperatures, is examined on its linear and weakly nonlinear stability. The analyses are conducted for small and moderate Prandtl numbers $0.001\le P\le 10$. Our attention is focused on a relatively low liquid bridge with $h/r_0=1$ where $h$ is the height and $r_0$ is the radius. The buoyancy effect is ignored and perfectly insulating condition is imposed on the surface of the liquid bridge. Linear stability analysis revealed that the critical condition was given by different azimuthal wavenumbers, $m=1$, 2, and 3, depending on the Prandtl number. The critical condition is given by steady solutions for $0 < P < 0.0578$ and by oscillatory solutions for $P > 0.0578$. Weakly nonlinear analysis identifies the stable region of the secondary solutions bifurcating from the linear critical curve. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R2.00006: Transient diffusive boundary layers in porous media: optimal perturbations Don Daniel, Nils Tilton, Amir Riaz We study the linear stability of gravitationally unstable, transient, diffusive boundary layers in porous media using nonmodal stability theory. We perform a classical optimization procedure to obtain perturbations with maximum subsequent amplification. Due to the transient base-state, optimal perturbations depend on the initial perturbation time. At small times, optimal perturbations extend beyond the boundary layer producing unphysical initial conditions. To reciprocate experimental conditions, we propose a modified optimization procedure using an adjoint-based optimization formulation that constrains the initial perturbation within the boundary layer. Interestingly, dominant wavenumbers obtained using resultant perturbations exhibit different temporal behavior in comparison to the classical scheme. We validate our results using nonlinear direct numerical simulations. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R2.00007: Transient diffusive boundary layers in porous media: The linear transition region Nils Tilton, Don Daniel, Amir Riaz Gravitationally unstable, transient, diffusive boundary layers play an important role in carbon dioxide sequestration in subsurface porous aquifers. Though the linear stability of these boundary layers has been studied extensively, there is little consensus concerning the critical time for instability. Nor is it clear which perturbations dominate the linear regime and trigger onset of convection due to nonlinear effects. We perform a comprehensive linear stability analysis using complementary quasi-steady and initial value problem approaches. We demonstrate that disagreement concerning the linear regime stems from an inherent sensitivity of the problem to how perturbation growth is measured. The perturbation concentration and velocity fields exhibit differing growth rates and these rates depend on the norm used to measure perturbation growth. Consequently, the critical time is not clearly defined. At later times, however, all initial perturbations tend towards the least stable quasi-steady eigenmode. We interpret this convergence process in terms of mechanisms related to the transient base-state, non-self-adjoint linear stability operator, and initial condition. Finally, we suggest potential paths for onset of convection which we demonstrate with direct numerical simulation. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R2.00008: Evaporation dynamics of ethanol drops under terrestrial and reduced gravity levels Florian Carle, Benjamin Sobac, David Brutin This experimental study, performed under microgravity conditions, focuses on the evaporation dynamics of ethanol drops and the formation and behaviour of the hydrothermal waves (HTWs) that spontaneously develop on the drops' surfaces. The aim of this study is to compare our results to a similar study performed under normal gravity conditions to confirm the purely thermocapillary origin of these instabilities. Under normal gravity conditions, a temperature gradient develops during the evaporation from the apex of the drop and the contact line, resulting in a gradient of surface tension, generating instabilities. HTWs flow radially around the apex where most of the evaporation takes place. In microgravity, the temperature gradient isn't as much defined as the one in normal gravity, but the apex maintains a temperature below the one of triple line. For different substrate temperatures and different levels of gravity, the HTWs follow a power law decay of the number of instabilities. Microgravity experiments show the same power law evolution. A scaling law succeed to predict with a good agreement the number of instabilities that form, regardless of the drop diameters, the substrate temperatures and the gravity levels. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R2.00009: Leidenfrost levitated liquid tori St\'ephane Perrard, Matthieu Labousse, Emmanuel Fort, John Bush, Yves Couder, Laurent Limat A drop of water deposited on a surface hotter than 150$^\circ$C can levitate without any contact with a solid container. Indeed the evaporation of the fluid generates a thin vapour film, which supports the drop's weight by lubrication forces (Leidenfrost effect). This effect was until now limited to droplets. We propose here an original substrate geometry, a circular brass through, that allows us to maintain in levitation any quantity of fluid. It could be a good tool to study wave propagation without solid boundary condition and thus very low friction. We report here one possible application, and our most striking observation : when the substrate temperature is high enough, convective motion appears in the liquid torus and its inner side becomes polygonal. This periodic deformation of large amplitude propagates along the azimuthal direction. The geometry, the flow and the shape appear very similar to the polygonal destabilization of an hydraulic jump. We propose here an experimental and theorical characterization of these rotating polygons having from three to twelve sides. Moreover, we have found a model describing the shape for any number of sides. It appears closely related to the Korteweg de Vries equation describing the propagation of solitonic waves in shallow water [Preview Abstract] |
Tuesday, November 20, 2012 2:57PM - 3:10PM |
R2.00010: Hydrodynamic Instabilities Produced by Evaporation Julio Cesar Ruben Romo-Cruz, Sergio Hernandez-Zapata, Gerardo Ruiz-Chavarria When a liquid layer (alcohol in the present work) is in an environment where its relative humidity is less than 100 percent evaporation appears. When RH is above a certain threshold the liquid is at rest. If RH decreases below this threshold the flow becomes unstable, and hydrodynamic cells develop. The aim of this work is to understand the formation of those cells and its main features. Firstly, we investigate how the cell size depends on the layer width. We also study how temperature depends on the vertical coordinate when the cells are present. An inverse temperature gradient is found, that is, the bottom of liquid layer is colder than the free surface. This shows that the intuitive idea that the cells are due to a direct temperature gradient, following a Marangoni-like process, does not work. We propose the hypothesis that the evaporation produce a pressure gradient that is responsible of the cell development. On the other hand, using a Schlieren technique we study the topography of the free surface when cells are present. Finally the alcohol vapor layer adjacent to the liquid surface is explored using scattering experiments, giving some insight on the plausibility of the hypothesis described previously. [Preview Abstract] |
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