1. Time evolution of thermal plumes in a three-dimensional enclosure due to heating from below at Rayleigh number = 1.06 106

Three-dimensional numerical predictions and experimental data have been obtained for natural convection from a 3 × 3 array of discrete heat sources flush-mounted on one vertical wall of a rectangular cavity and cooled by the opposing wall. Predictions performed in a companion paper (Heindel et al., 1995a) revealed that three-dimensional edge effects are significant and that, with increasing Rayleigh number, flow and heat transfer become more uniform across each heater face. The three-dimensional predictions are in excellent agreement with the data of this study, whereas a two-dimensional model of the experimental geometry underpredicts average heat transfer by as much as 20 percent. Experimental row-averaged Nusselt numbers are well correlated with a Rayleigh number exponent of 0.25 for RaLz ≲ 1.2 × 108.

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Plume formation and resonant bifurcations in porous-media convection

Journal of Fluid Mechanics ◽

10.1017/s0022112094004386 ◽

1994 ◽

Vol 272 ◽

pp. 67-90 ◽

Cited By ~ 34

Author(s):

Michael D. Graham ◽

Paul H. Steen

Keyword(s):

Boundary Layer ◽

Porous Media ◽

Rayleigh Number ◽

Scaling Laws ◽

Thermal Plumes ◽

Scaling Behaviour ◽

Parametric Resonances ◽

Classical Boundary ◽

Rayleigh Benard Convection ◽

Rayleigh Benard

The classical boundary-layer scaling laws proposed by Howard for Rayleigh–Bénard convection at high Rayleigh number extend to the analogous case of convection in saturated porous media. We computationally study two-dimensional porous-media convection near the onset of this scaling behaviour. The main result of the paper is the observation and study of instabilities that lead to deviations from the scaling relations.At Rayleigh numbers below the scaling regime, boundary-layer fluctuations born at a Hopf bifurcation strengthen and eventually develop into thermal plumes. The appearance of plumes corresponds to the onset of the boundary-layer scaling behaviour of the oscillation frequency and mean Nusselt number, in agreement with the classical theory. As the Rayleigh number increases further, the flow undergoes instabilities that lead to ‘bubbles’ in parameter space of quasi-periodic flow, and eventually to weakly chaotic flow. The instabilities disturb the plume formation process, effectively leading to a phase modulation of the process and to deviations from the scaling laws. We argue that these instabilities correspond to parametric resonances between the timescale for plume formation and the characteristic convection timescale of the flow.

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Study of a temperature gradient metamorphism of snow from 3-D images: time evolution of microstructures, physical properties and their associated anisotropy

The Cryosphere ◽

10.5194/tc-8-2255-2014 ◽

2014 ◽

Vol 8 (6) ◽

pp. 2255-2274 ◽

Cited By ~ 27

Author(s):

N. Calonne ◽

F. Flin ◽

C. Geindreau ◽

B. Lesaffre ◽

S. Rolland du Roscoat

Keyword(s):

Temperature Gradient ◽

Physical Properties ◽

Time Evolution ◽

Three Dimensional ◽

Vertical Direction ◽

Large Set ◽

Correlation Lengths ◽

Snow Properties ◽

Cold Room ◽

Anisotropy Coefficients

Abstract. We carried out a study to monitor the time evolution of microstructural and physical properties of snow during temperature gradient metamorphism: a snow slab was subjected to a constant temperature gradient in the vertical direction for 3 weeks in a cold room, and regularly sampled in order to obtain a series of three-dimensional (3-D) images using X-ray microtomography. A large set of properties was then computed from this series of 3-D images: density, specific surface area, correlation lengths, mean and Gaussian curvature distributions, air and ice tortuosities, effective thermal conductivity, and intrinsic permeability. Whenever possible, specific attention was paid to assess these properties along the vertical and horizontal directions, and an anisotropy coefficient defined as the ratio of the vertical over the horizontal values was deduced. The time evolution of these properties, as well as their anisotropy coefficients, was investigated, showing the development of a strong anisotropic behavior during the experiment. Most of the computed physical properties of snow were then compared with two analytical estimates (self-consistent estimates and dilute beds of spheroids) based on the snow density, and the size and anisotropy of the microstructure through the correlation lengths. These models, which require only basic microstructural information, offer rather good estimates of the properties and anisotropy coefficients for our experiment without any fitting parameters. Our results highlight the interplay between the microstructure and physical properties, showing that the physical properties of snow subjected to a temperature gradient cannot be described accurately using only isotropic parameters such as the density and require more refined information. Furthermore, this study constitutes a detailed database on the evolution of snow properties under a temperature gradient, which can be used as a guideline and a validation tool for snow metamorphism models at the micro- or macroscale.

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Spectral properties of magnetohydrodynamic convection with mean horizontal temperature gradient

Proceedings of the International Astronomical Union ◽

10.1017/s1743921307001032 ◽

2006 ◽

Vol 2 (S239) ◽

pp. 513-513

Author(s):

D. Skandera ◽

W.-Ch. Müller

Keyword(s):

Temperature Field ◽

Rayleigh Number ◽

Temperature Gradient ◽

Numerical Simulations ◽

Spectral Properties ◽

Three Dimensional ◽

Numerical Code ◽

Dimensional System ◽

Horizontal Temperature Gradient ◽

Mhd Turbulence

AbstractSpectral properties of convective magnetohydrodynamic (MHD) turbulence in two and three dimensions are studied by means of direct numerical simulations (Skandera D. & Müller W.-C. 2006). The investigated system is set up with a mean horizontal temperature gradient in order to avoid a development of elevator instabilities in a fully periodic box. All simulations are performed without mean magnetic field. The applied resolution is 5123 and 20482. The MHD equation are solved by a numerical code (Müller & Biskamp 2000) that uses a standard pseudospectral scheme. For removing of aliasing errors a spherical truncation method is employed. Obtained results are compared with predictions of various existing phenomenological theories for magnetohydrodynamic and convective turbulence (Müller & Biskamp 2000). While the three-dimensional system is found to operate in a Kolmogorov-like regime where buoyant forces have a negligible impact on the turbulence dynamics (relatively low Rayleigh number achieved in the simulation; Ra ∼106), the two-dimensional system exhibits interesting irregular quasi-oscillations between a buoyancy dominated Bolgiano-Obukhov-like regime of turbulence and a standard Iroshnikov-Kraichnan-like regime of turbulence (Müller & Biskamp 2000). The most important parameter determining the turbulent regime of 2D magnetoconvection, apart from a high Rayleigh number, seems to be the mutual alignment of velocity and magnetic fields. The non-linear dynamics and the interplay between individual fields are examined with different transfer functions that confirm basic assumptions about directions of energy transfer in spectral space. Kinetic, magnetic and temperature energy are transported by a turbulent cascade from large to smaller scales. The local/nonlocal character of the transport is tested for several individual terms in the governing equations. Moreover, other statistical quantities, e.g. probability density functions, are computed as well. A passive character of the temperature field in the investigated three-dimensional magnetoconvection is supported by computations of intermittency using extended self-similarity. The intermittency of the Elsasser field z+ is in agreement with results from numerical simulations of isotropic MHD turbulence (Müller & Biskamp 2000). The intermittency of the temperature field is found to approximately agree with results of passive scalar measurements in hydrodynamic turbulence (Ruiz-Chavarria, Baudet & Ciliberto 1996).

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Time evolution of companies towards a stable scaling curve obtained from flow diagrams in three-dimensional phase space

New Journal of Physics ◽

10.1088/1367-2630/ab0e55 ◽

2019 ◽

Vol 21 (4) ◽

pp. 043038

Author(s):

Yuh Kobayashi ◽

Hideki Takayasu ◽

Shlomo Havlin ◽

Misako Takayasu

Keyword(s):

Phase Space ◽

Time Evolution ◽

Three Dimensional ◽

Dimensional Phase Space ◽

Flow Diagrams

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Convection in a box: linear theory

Journal of Fluid Mechanics ◽

10.1017/s0022112067001545 ◽

1967 ◽

Vol 30 (3) ◽

pp. 465-478 ◽

Cited By ~ 237

Author(s):

Stephen H. Davis

Keyword(s):

Rayleigh Number ◽

Linear Stability ◽

Linear Theory ◽

Cross Sections ◽

Critical Rayleigh Number ◽

Three Dimensional ◽

Wave Number ◽

Spatial Variables ◽

Zero Velocity ◽

The Cross

The linear stability of a quiescent, three-dimensional rectangular box of fluid heated from below is considered. It is found that finite rolls (cells with two non-zero velocity components dependent on all three spatial variables) with axes parallel to the shorter side are predicted. When the depth is the shortest dimension, the cross-sections of these finite rolls are near-square, but otherwise (in wafer-shaped boxes) narrower cells appear. The value of the critical Rayleigh number and preferred wave-number (number of finite rolls) for a given size box is determined for boxes with horizontal dimensions h, ¼ ≤ h/d ≤ 6, where d is the depth.

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Three-dimensional instability of axisymmetric buoyant convection in cylinders heated from below

Journal of Fluid Mechanics ◽

10.1017/s0022112096008373 ◽

1996 ◽

Vol 326 ◽

pp. 399-415 ◽

Cited By ~ 47

Author(s):

M. Wanschura ◽

H. C. Kuhlmann ◽

H. J. Rath

Keyword(s):

Rayleigh Number ◽

Linear Stability ◽

Critical Rayleigh Number ◽

Three Dimensional ◽

Base Flow ◽

Onset Of Convection ◽

Buoyant Convection ◽

Thermal Boundary Conditions ◽

Aspect Ratios ◽

Prandtl Numbers

The stability of steady axisymmetric convection in cylinders heated from below and insulated laterally is investigated numerically using a mixed finite-difference/Chebyshev collocation method to solve the base flow and the linear stability equations. Linear stability boundaries are given for radius to height ratios γ from 0.9 to 1.56 and for Prandtl numbers Pr = 0.02 and Pr = 1. Depending on γ and Pr, the azimuthal wavenumber of the critical mode may be m = 1, 2, 3, or 4. The dependence of the critical Rayleigh number on the aspect ratio and the instability mechanisms are explained by analysing the energy transfer to the critical modes for selected cases. In addition to these results the onset of buoyant convection in liquid bridges with stress-free conditions on the cylindrical surface is considered. For insulating thermal boundary conditions, the onset of convection is never axisymmetric and the critical azimuthal wavenumber increases monotonically with γ. The critical Rayleigh number is less then 1708 for most aspect ratios.

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