Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session E2: Convection and Buoyancy-Driven Flows III: Thermal Instability |
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Chair: Jerzy M. Floryan, University of Western Ontario Room: 324 |
Sunday, November 24, 2013 4:45PM - 4:58PM |
E2.00001: Stability transitions and energy pathways in horizontal convection at large Rayleigh numbers Bishakhdatta Gayen, Ross W. Griffiths, Graham O. Hughes We report three-dimensional convective circulation forced by a temperature gradient along the surface of a rectangular channel, using direct and large eddy simulations over a wide range of Rayleigh numbers, $Ra\sim 10^8-10^{15}$. The solutions are allowed to reach thermal equilibrium in which there is no net heat input. A sequence of several stability transitions lead to a change from laminar to fully-developed turbulent flow. At the smallest $Ra$ convection is maintained by a balance of viscous and buoyancy forces inside the thermal boundary layer, whereas at the largest $Ra$ inertia dominates over viscous stresses. This results in an enhancement of the overall heat transfer at $Ra\ge10^{10}$, while both dynamical balances give $Nu\sim Ra^{1/5}$. Our main focus is to analyze the mechanical energy budget. Below the transition the small scales of motion are driven predominately by thermal convection, whereas at $Ra > 10^{13}$ shear plays a dominant role in sustaining the small-scale turbulence. [Preview Abstract] |
Sunday, November 24, 2013 4:58PM - 5:11PM |
E2.00002: Instabilities of Natural Convection in a Periodically Heated Layer M.Z. Hossain, Jerzy M. Floryan Natural convection in a horizontal layer subject to a spatially periodic heating along the lower wall has been investigated. The heating produces sinusoidal temperature variations characterized by the wave number $\alpha $ and the Rayleigh number Ra$_{\mathrm{p}}$. The primary response has the form of stationary rolls with axis orthogonal to the heating wave vector. For large $\alpha $ convection is limited to a thin layer adjacent to the lower wall with a uniform conduction above it. Linear stability was used to determine conditions leading to a secondary convection. Two mechanisms of instability have been identified. For $\alpha =$0(1), the parametric resonance dominates and leads to the pattern of instability that is locked-in with the pattern of the heating according to the relation $\delta _{\mathrm{cr}} = \alpha $/2, where $\delta_{\mathrm{cr}}$ denotes the component of the critical disturbance wave vector parallel to the heating wave vector. The second mechanism, Rayleigh-B\'{e}nard (RB) mechanism, dominates for large $\alpha $. Competition between these mechanisms gives rise to non-commensurable states and appearance of soliton lattices, to the formation of distorted transverse rolls, and to the appearance of the wave vector component in the direction perpendicular to the forcing direction. [Preview Abstract] |
Sunday, November 24, 2013 5:11PM - 5:24PM |
E2.00003: On the transition to chaos of natural convection between two infinite differentially heated vertical plates Zhenlan Gao, Berengere Podvin, Anne Sergent, Shihe Xin, Patrick le Quere, Laurette Tuckerman Natural convection of air between two infinite vertical differentially heated plates is studied analytically in two dimensions (2D) and numerically in two and three dimensions (3D), for Rayleigh numbers Ra up to three times the critical value $Ra_c$. The first instability is a supercritical circle pitchfork bifurcation leading to steady 2D corotating rolls. A Ginzburg-Landau equation is derived analytically for the flow around this first bifurcation and compared with results from direct numerical simulation (DNS). In 2D, DNS shows that the rolls become unstable via a Hopf bifurcation. As $Ra$ is further increased, the flow becomes quasi-periodic, then temporally chaotic for a limited range of Rayleigh numbers, beyond which the flow returns to a steady state through a spatial modulation instability. In 3D, the rolls instead undergo another pitchfork bifurcation to 3D structures, which consist of transverse rolls connected by counter-rotating vorticity braids. The flow then becomes time-dependent through a Hopf bifurcation, as exchanges of energy occur between the rolls and the braids. Chaotic behavior subsequently occurs through two competing mechanisms: a sequence of period-doubling bifurcations leading to intermittency or else a spatial pattern modulation. [Preview Abstract] |
Sunday, November 24, 2013 5:24PM - 5:37PM |
E2.00004: Spanwise plumes in wakes behind heated cylinder Ajith Kumar S, Anil Lal S, Sameen A 3D wake transition in flow past cylinder is interesting theoretically and industrially. A three dimensional Finite volume computation has been performed on an incompressible flow past heated cylinder to understand the wake behavior behind the cylinder, under the Boussinesq assumption. We study the heat transfer characteristics and the coherent structures behind the cylinder at different Prandtl numbers. In forced convection, the 3D transition occurs above Reynolds number, Re=180-190 (Re is based on the cylinder diameter). However, the present 3D computational analyses show that in mixed convection, the so called ``mode-E'' instability (3D transition of wake behind the cylinder caused by the heating of the cylinder) happens at a much lower Reynolds number. The co-existence of mushroom like coherent structures called the plumes along with the shed vortices is observed for a range of heating conditions. These plumes originates from the core of the upper vortex rows at a definite span wise wavelengths. The dependence of Prandtl number on the span wise wavenumber of these plumes is also analyzed. [Preview Abstract] |
Sunday, November 24, 2013 5:37PM - 5:50PM |
E2.00005: Plate-like convection in fluids with temperature-dependent viscosity Ana M. Mancho, Jezabel Curbelo The study of instabilities in fluids in which viscosity experiences a transition at a certain temperature range is of great interest for the understanding of planetary interiors, since this phenomena models the melting and solidification of a magma ocean and thus is suitable for representing a lithosphere over a convecting mantle. To this end, we study a 2D convection problem in which viscosity depends on temperature by abruptly changing its value by a factor 400 within a narrow temperature gap at which magma melts. We perform a study which combines bifurcation analysis and time dependent simulations. Solutions such as limit cycles are found that are fundamentally related to the presence of the O(2) symmetry. Sporadically during these cycles, through abrupt bursts, spontaneous plate-like behaviors that rapidly evolve towards a stagnant lid regime emerge. The plate-like evolution alternates motions towards either right or left, introducing temporary asymmetries on the convecting styles. Further time dependent regimes are described for different transition laws which are greatly influenced by the presence of the symmetry. [Preview Abstract] |
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