Convection in boxes: an experimental investigation in vertical cylinders and annuli

Stork, K.; Müller, Ulrich

doi:10.1017/s0022112075002534

Cited by 82 publications

(27 citation statements)

References 10 publications

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“…they are trigonometric in the azimuthal angle. But at higher Ra, the patterns form rolls, bending and pinching so as to fit into the cylinder.The instability of the conductive state in a cylindrical geometry was well established in the 1970s-1980s [3][4][5][6]. Critical Rayleigh numbers Ra c are about 2000 for Γ ∼ 1, increasing steeply for lower Γ and decreasing asymptotically towards Ra c = 1708 for Γ → ∞.…”

mentioning

confidence: 93%

Extreme multiplicity in cylindrical Rayleigh-Bénard convection. I. Time dependence and oscillations

Boronska

Tuckerman

2010

Phys. Rev. E

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Rayleigh-Bénard convection in a cylindrical container can take on many different spatial forms. Motivated by the results of Hof [Phys. Fluids 11, 2815 (1999)], who observed coexistence of several stable states at a single set of parameter values, we have carried out simulations at the same Prandtl number, that of water, and a radius-to-height aspect ratio of two. We have used two kinds of thermal boundary conditions: perfectly insulating sidewalls and perfectly conducting sidewalls. In both cases we obtain a wide variety of coexisting steady and time-dependent flows.

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confidence: 93%

Extreme multiplicity in cylindrical Rayleigh-Bénard convection. I. Time dependence and oscillations

Boronska

Tuckerman

2010

Phys. Rev. E

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“…The critical Rayleigh number for the onset of convection increases with this ratio, according to both theory Sani, 1970, 1971;Rosenblat, 1982] and experiments [Stork and Müller, 1975]. In these studies, rigid tank walls impose no-slip boundary conditions at the edges of the unstable layer.…”

Section: Convective Instability Of a Block Of Finite Widthmentioning

confidence: 74%

“…For our present purposes, we need only refer to large Prandtl number fluids and aspect ratios that are much less than 1, typically 0.1. The critical Rayleigh number for the onset of convection increases with this ratio, according to both theory Sani, 1970, 1971;Rosenblat, 1982] and experiments [Stork and Müller, 1975]. Different planforms are generated depending on the thermal boundary conditions at the side walls.…”

Section: Convective Instability Of a Block Of Finite Widthmentioning

confidence: 76%

Generation of continental rifts, basins, and swells by lithosphere instabilities

et al. 2013

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Continents may be affected simultaneously by rifting, uplift, volcanic activity, and basin formation in several different locations, suggesting a common driving mechanism that is intrinsic to continents. We describe a new type of convective instability at the base of the lithosphere that leads to a remarkable spatial pattern at the scale of an entire continent. We carried out fluid mechanics laboratory experiments on buoyant blocks of finite size that became unstable due to cooling from above. Dynamical behavior depends on three dimensionless numbers, a Rayleigh number for the unstable block, a buoyancy number that scales the intrinsic density contrast to the thermal one, and the aspect ratio of the block. Within the block, instability develops in two different ways in an outer annulus and in an interior region. In the outer annulus, upwellings and downwellings take the form of periodically spaced radial spokes. The interior region hosts the more familiar convective pattern of polygonal cells. In geological conditions, such instabilities should manifest themselves as linear rifts striking at a right angle to the continent‐ocean boundary and an array of domal uplifts, volcanic swells, and basins in the continental interior. Simple scaling laws for the dimensions and spacings of the convective structures are derived. For the subcontinental lithospheric mantle, these dimensions take values in the 500–1000 km range, close to geological examples. The large intrinsic buoyancy of Archean lithospheric roots prevents this type of instability, which explains why the widespread volcanic activity that currently affects Western Africa is confined to post‐Archean domains.

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“…While T is measured with high precision, the instability in the unforced reference cell can occur at slightly smaller T c than in an infinitely extended system, due to the rather small aspect ratio (see e.g. Stork & Müller 1975;Brown & Stewartson 1978;Cross & Hohenberg 1993). This would lead to an overestimation of the cell height and of q f /q c .…”

Section: Summary and Discussionmentioning

confidence: 99%

Resonance patterns in spatially forced Rayleigh–Bénard convection

2014

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We report on the influence of a quasi-one-dimensional periodic forcing on the pattern selection process in Rayleigh-Bénard convection (RBC). The forcing was introduced by a lithographically fabricated periodic texture on the bottom plate. We study the convection patterns as a function of the Rayleigh number (Ra) and the dimensionless forcing wavenumber (q f ). For small Ra, convection takes the form of straight parallel rolls that are locked to the underlying forcing pattern. With increasing Ra, these rolls give way to more complex patterns, due to a secondary instability. The forcing wavenumber q f was varied in the experiment over the range of 0.6q c < q f < 1.4q c , with q c being the critical wavenumber of the unforced system. We investigate the stability of straight rolls as a function of q f and report patterns that arise due to a secondary instability.

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Convection in boxes: an experimental investigation in vertical cylinders and annuli

Cited by 82 publications

References 10 publications

Extreme multiplicity in cylindrical Rayleigh-Bénard convection. I. Time dependence and oscillations

Extreme multiplicity in cylindrical Rayleigh-Bénard convection. I. Time dependence and oscillations

Generation of continental rifts, basins, and swells by lithosphere instabilities

Resonance patterns in spatially forced Rayleigh–Bénard convection

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