Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session LU: Convection and Buoyancy Driven Flows V |
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Chair: Brent Houchens, Rice University Room: Hilton Chicago Marquette |
Tuesday, November 22, 2005 8:00AM - 8:13AM |
LU.00001: Particle Tracking in Rotating Rayleigh-Benard Convection Janet Scheel, Paul Fischer Aref [J. Fluid Mech., 1984] developed the concept of chaotic advection by utilizing the fact that real space is phase space for a two-dimensional fluid. This analysis is extended to investigate large aspect ratio, 3-D rotating Rayleigh-Benard convection with no-slip boundary conditions. Numerical results for the real space evolution of tracer particles provides us with a means to study the transition to the domain chaos state. The idealized domain chaos state is characterized by a steady Kuppers-Lortz switching from a set of rolls with one orientation to a set of rolls in a different orientation. This system is compared and contrasted with the blinking roll model of chaotic advection presented by Mullowney et. al. [SIAM Applied Dynamical Systems, 2005]. [Preview Abstract] |
Tuesday, November 22, 2005 8:13AM - 8:26AM |
LU.00002: Spiral instabilities in a non-homogeneously heated fluid in cylindrical geometry Ana Maria Mancho, Maria Cruz Navarro, Henar Herrero$^3$ We present results on the instabilities that appear in a fluid which is in a cylindrical container when a localized Gaussian-like heating around the origin is applied at the bottom. The instability is due to buoyant effects either with radial or vertical gravity. As soon as the horizontal thermal gradient is non-zero a stationary basic state sets in. In contrast to classical Rayleigh-Bernard convection several heat related parameters --not just the vertical temperature gradient-- control the stability of the basic flow. We discuss bifurcations that at finite Prandtl number appear for different values of these parameters. In particular we find that spiral waves may appear in some cases. Spirals traditionally have been related to chaotic solutions in Rayleigh-Bernard convection. In our work we show spirals that are linearly growing structures of stationary basic solutions under certain heat conditions. Other instabilities are also discussed. [Preview Abstract] |
Tuesday, November 22, 2005 8:26AM - 8:39AM |
LU.00003: Patterns in cylindrical Rayleigh-Benard convection Katarzyna Boronska, Laurette S. Tuckerman We simulate the Boussinesq equations for Rayleigh-B\'{e}nard convection in a cylindrical container of aspect ratio {\it radius}$/${\it height}$=2$ and either perfectly insulating or perfectly conducting sidewalls. We investigate the phenomenon of coexisting stable states for a fluid with Prandtl number $6.7$. Varying initial conditions, we obtain various convective patterns for the same Rayleigh number. The results for perfectly insulating sidewalls are in good agreement with experiment of Hof {\it et~al}. We follow the stationary solutions using a steady-state solver and obtain a bifurcation diagram covering the range of Rayleigh numbers from convection onset up to $Ra=30\,000$. [Preview Abstract] |
Tuesday, November 22, 2005 8:39AM - 8:52AM |
LU.00004: WITHDRAWN: Compressibility effects on the onset of convection in the Rayleigh-B\'{e}nard problem Avshalom Manela, Itzchak Frankel For the onset of convection in a compressible fluid in a Rayleigh-B\'{e}nard setup the adiabatic expansion of a fluid element rising through the reference hydrostatic pressure field needs to reduce its density below the ambient reference value. This condition is initially satisfied at the upper wall when the Froude number attains some minimal value, $Fr=Fr_{0}$. Recent studies based on nonlinear simulations of the initial-value problem and linear stability analyses indicate that, with decreasing $\delta=(Fr-Fr_0)/Fr_0$, convection is confined to an increasingly narrower domain adjacent to the upper wall while the corresponding wavenumber becomes increasingly large. These observations are correlated with the above necessary condition via a linear temporal stability analysis for a perfect gas in the limit $\delta\ll1$ under arbitrary temperature differences. Transition to convection is governed by a single equation for the vertical velocity. This equation differs from the familiar Boussinesq equation in that the `Rayleigh term' is replaced by a term which is linearly dependent upon the vertical coordinate. Making use of an integral representation we apply the method of steepest descents to satisfy the boundary conditions thereby obtaining the requisite eigenvalue problem. The results showing the width of the convection domain and the critical wavenumber as $O(\delta)$ and $O(\delta^{-1})$, respectively, are in remarkable agreement with those appearing in the literature. [Preview Abstract] |
Tuesday, November 22, 2005 8:52AM - 9:05AM |
LU.00005: Non-Oberbeck-Boussinesq effects on the boundary-layer thicknesses Francisco Fontenele Araujo, Siegfried Grossmann, Detlef Lohse A measure characterizing non-Oberbeck-Boussinesq effects in Rayleigh-Benard convection is the ratio $\lambda_{bottom}/\lambda_{top}$ between the thicknesses of the boundary-layers formed at the thermal plates (bottom and top). In the present work, we discuss an extension of Prandtl-Pohlhausen theory accounting for height-dependent viscosities and thermal diffusivities. [Preview Abstract] |
Tuesday, November 22, 2005 9:05AM - 9:18AM |
LU.00006: Overturning in a cylindrical filling box Nigel Kaye, Gary Hunt We examine the overturning in a cylindrical `filling box' driven by a single axisymmetric point source turbulent plume. We measure the initial penetration depth (\(h\)) of the buoyant flow that intrudes vertically up the side wall as a function of the box radius (\(R\)) and height \((H\)). Dimensional arguments reduce the problem to finding \(\eta=h/H\) as a function of the aspect ratio \(\Phi=R/H\). We model the flow in two parts, the radial outflow from the plume along the base of the box and the flow up the side wall. The outflow is modelled as a forced constant buoyancy flux radial gravity current while the side- wall flow is modelled as a turbulent line fountain. Different flow regimes were found for small and large aspect ratios. Firstly, for small aspect ratios, the plume outflow is still adjusting toward a pure gravity current on impact with the vertical wall. For this regime the dimensionless rise height is given by \(\eta \sim \Phi^{-1/3}\). Secondly, for larger aspect ratios, the outflow is fully developed before impact. In this case the rise height is given by \(\eta \sim Const\). Experimental results show good agreement with these scalings. [Preview Abstract] |
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