Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session BJ: Convection and Buoyancy-Driven Flows II* |
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Chair: Maria Cruz Navarro, University of Castilla-La Mancha Room: Tampa Marriott Waterside Hotel and Marina Meeting Room 6 |
Sunday, November 19, 2006 11:00AM - 11:13AM |
BJ.00001: Complex dynamics in binary mixture convection with weak negative Soret coupling Oriol Batiste, Arantxa Alonso, Isabel Mercader Thermal convection in a binary fluid layer heated from below is a system that exhibits a great variety of pattern forming phenomena when driven away from equilibrium. Results on direct numerical simulations of convection in binary fluids in large aspect ratio containers are presented. Periodic boundary conditions have been considered in the horizontal direction, modelling the annular cells frequently used in experiments. We have focused on binary mixtures with negative values of the separation ratio $S$, for which the primary bifurcation is subcritical and oscillatory, and with weak Soret coupling ($S$ close to zero), so that nonlinear dispersion is important. Highly resolved spectral methods were used to solve the hydrodynamic equations in the two-dimensional approximation. The weakly nonlinear states arising very close to the onset of convection, the strongly nonlinear bursts of amplitude that precede the small-amplitude states, and the dispersive chaotic states encountered further above onset in experiments for mixtures with a weak negative Soret coupling, are analyzed in detail in extended domains of aspect ratio $\Gamma=80$. Steady localized states surrounded either by quiescent fluid or by small-amplitude waves are also obtained, and the role they play in the dynamics is elucidated. Our numerical study using the full convection equations completes former experimental and numerical works on such states. [Preview Abstract] |
Sunday, November 19, 2006 11:13AM - 11:26AM |
BJ.00002: Symmetry breaking of the onset of convection in a rotating spherical gap Antje Brucks The technique of particle image velocimetry is used to study the natural convection in a rotating spherical gap of $r_1/r_2=0.4$ filled with silicon oil. The main subject of the study is the symmetry breaking with increasing rotation rate. Our measurements are conducted for Rayleigh numbers $10^5 < Ra < 10^7$ and Taylor numbers up to $Ta = 10^6$. Starting at $m=2$, the mode number of the retrograde drifting vortices is increasing with Taylor number. The three dimensional vortex structures are characterized by their time dependent velocity and vorticity fields. We can show that the symmetry breaking is a Hopf bifurcation. However, as the vortex dynamics is influenced by a combination of centrifugal and Coriolis effects it shows a complex behaviour. [Preview Abstract] |
Sunday, November 19, 2006 11:26AM - 11:39AM |
BJ.00003: Gravity currents near the density maximum David Leppinen, Antony Kay We describe lock-release experiments in which the receiving water is close to the freezing point, and is denser than the warm water in the lock. Experiments are performed with either a free surface or a rigid lid, the latter with a view to simulating warm water releases into ice-covered lakes. When the lock gate is removed, a gravity current of warm water flows out from the lock along the top of the receiving water. Mixing at the interface creates water that is denser than the ambient, which is detrained and sinks to the bed of the channel. Eventually, sufficient cold water is entrained into the gravity current for it to lose all of its buoyancy. At this stage, the gravity current is arrested, after which the only motion is vertical convection. The progress and eventual arrest of the current is described using a box model which incorporates a simple parameterisation of entrainment. [Preview Abstract] |
Sunday, November 19, 2006 11:39AM - 11:52AM |
BJ.00004: Study on Coherent Structure of Turbulent Thermal Convection by Simultaneous Measurement of Temperature and Velocity by Liquid Crystal Tracers Nobuyuki Fujisawa, Masataka Watanabe, Yuji Hashizume In order to understand the formation and the development of the plume structure in turbulent thermal convection, the temporal and spatial variations of temperature and velocity field are measured in the non-penetrative thermal convection of the horizontal fluid layer using the combined liquid crystal thermometry and stereo-velocimetry. It is found that the spoke structure is generated near the heated surface and moves along the heated surface unsteadily changing the cell size. The thermal plume is generated from the high temperature region of the spoke structure, where the vertical velocity component is clearly observed near the heated surfaces. [Preview Abstract] |
Sunday, November 19, 2006 11:52AM - 12:05PM |
BJ.00005: A class of boundary-layer problems for buoyancy-driven motions near a density maximum Howard Stone, Emilie Dressaire, Ernst van Nierop Engineering and design questions are becoming increasingly important for applications in the waters of the deep ocean where the temperature is close to the point of the maximum density of water. Here we treat a class of boundary-layer problems based on the nonlinear Boussinesq approximation appropriate for the conditions near a density maximum. Pioneering work in the area was performed by Goren (1966) and Gebhart and colleagues (in the 1970s-80s). We present results of the boundary-layer type for a wide range of physically relevant flow situations and contrast the results with known solutions based on the linearized Boussinesq approximation. [Preview Abstract] |
Sunday, November 19, 2006 12:05PM - 12:18PM |
BJ.00006: Spiral instabilities in Rayleigh-Benard due to a localized heating Henar Herrero, Mar\'ia Cruz Navarro, Ana Mar\'ia Mancho We study from the numerical point of view, instabilities developed in a fluid layer with a free surface, in a cylindrical container which at the bottom has a heating spike modelled by a parameter $\beta$. This localised heating approaches a boundary condition for a thermal plume. The partial differential equations that model this problem are discretized with a Chebyshev collocation method with appropiate conditions for the pressure field. An axysimmetric basic state appears as soon as a non-zero lateral temperature gradient is imposed. A preconditioned Arnoldi method has been used to compute the eigenvalues for the linear stability analysis. The basic state may bifurcate to different solutions depending on vertical and lateral temperature gradients and on the shape of the heating. We find different kinds of instabilities: extended patterns growing on the whole domain which include those known as target and spiral waves. Localised structures both at the origin and at the outer part of the cylinder may appear either as Hopf or stationary bifurcations. [Preview Abstract] |
Sunday, November 19, 2006 12:18PM - 12:31PM |
BJ.00007: Rotating convection: the influence of centrifugal buoyancy Francisco Marques, Juan Lopez, Oriol Batiste, Isabel Mercader Rotating convection is analyzed in a cylinder of aspect ratio one. Traditionally, density variation was only incorporated in the gravitational and not in the centrifugal buoyancy term. In this limit the governing equations admit a trivial conduction solution. The presence of centrifugal buoyancy changes the problem in a fundamental manner. The buoyancy force has a radial component that destroys the horizontal translation invariance assumed in the unbounded theoretical treatments of the problem and the $Z_2$ reflection symmetry about the cylinder mid-height. The centrifugal buoyancy drives a large scale circulation in which the cool denser fluid is centrifuged radially outward and the hot less dense fluid is centrifuged radially inward, and so there is no trivial conduction state when centrifugal buoyancy is incorporated. For small Froude numbers the transition to 3D flow happens around $Ra\approx 7,500$. For Froude numbers larger than 3, the centrifugal buoyancy delays transition to $Ra\approx 50,000$. At intermediate $Fr$ the transition to 3D flow happens via four different Hopf bifurcations, resulting in different coexisting branches of 3D solutions with complex interactions. How the centrifugal and the gravitational buoyancies compete, and the transition to 3D flow is different along each branch. The main conclusion is that centrifugal buoyancy changes quantitatively and qualitatively the flow dynamics. [Preview Abstract] |
Sunday, November 19, 2006 12:31PM - 12:44PM |
BJ.00008: Asymptotic analysis of strongly nonlinear Rayleigh--B\'{e}nard convection and Langmuir circulation Greg Chini Matched asymptotic analysis and global conservation constraints are used to obtain a semi-analytic yet strongly nonlinear description of two related flows: (i) Rayleigh--B\'{e}nard convection at O(1) Prandtl number, and (ii) Langmuir circulation (LC), a wind- and wave-driven convective flow. The analysis, which is carried out in the strong-forcing/weak-diffusion limit, extends previous studies of large Rayleigh number, infinite Prandtl number (i.e. fast but viscous) convection and related analyses of magnetic flux expulsion by eddies. Here, the velocity field is obtained by solving the full nonlinear momentum equation rather than by integrating a linear version or by being specified \emph{a priori}. In marked contrast to weakly nonlinear convection cells, the laminar roll-vortex solutions furnished by the analysis exhibit flow features relevant to turbulent convection, including the complete vertical re-distribution of the basic-state temperature (or, for LC, downwind velocity) field. Comparisons with well-resolved pseudospectral numerical simulations confirm the accuracy of the asymptotic results. [Preview Abstract] |
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