Diffusion transients in convection rolls

This paper first describes an apparatus for measuring the Nusselt number N versus the Rayleigh number R of convecting normal liquid 4He layers. The most important feature of the apparatus is its ability to provide layers of different heights d, and hence different aspect ratios [Gcy ]. The horizontal cross-section of each layer is circular, and [Gcy ] is defined by [Gcy ] = D/2d where D is the diameter of the layer. We report results for 2.4 [les ] [Gcy ] [les ] 16 and for Prandtl numbers Pr spanning 0.5 [lsim ] Pr [lsim ] 0.9 These results are presented in terms of the slope N1 = RcdN/dR evaluated just above the onset of convection at Rc. We find that N1 is only a slowly increasing function of [Gcy ] in the range 6 [lsim ] [Gcy ] [lsim ] 16, and that it has a value there which is quite close to 0.72. This value of N1 is in good agreement with variational calcuations by Ahlers et al. (1981) pertinent to parallel convection rolls in cylindrical geometry. Particularly for [Gcy ] [lsim ] 6, we find additional small-scale structure in N1 associated with changes in the number of convection rolls with changing [Gcy ]. An additional test of the linearzied hydrodynamics is given by measurements of Rc. We find good agreement between theory and our data for Rc.

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Spatial Heterogeneity and Imperfect Mixing in Chemical Reactions: Visualization of Density-Driven Pattern Formation

Research Letters in Physical Chemistry ◽

10.1155/2009/350424 ◽

2009 ◽

Vol 2009 ◽

pp. 1-4 ◽

Cited By ~ 1

Author(s):

Sabrina G. Sobel ◽

Harold M. Hastings ◽

Matthew Testa

Keyword(s):

Pattern Formation ◽

Salt Water ◽

Model System ◽

Reaction Vessel ◽

Chemical System ◽

Industrial Processes ◽

History Of ◽

Convection Rolls ◽

Belousov Zhabotinsky Reaction ◽

Complex Ion

Imperfect mixing is a concern in industrial processes, everyday processes (mixing paint, bread machines), and in understanding salt water-fresh water mixing in ecosystems. The effects of imperfect mixing become evident in the unstirred ferroin-catalyzed Belousov-Zhabotinsky reaction, the prototype for chemical pattern formation. Over time, waves of oxidation (high ferriin concentration, blue) propagate into a background of low ferriin concentration (red); their structure reflects in part the history of mixing in the reaction vessel. However, it may be difficult to separate mixing effects from reaction effects. We describe a simpler model system for visualizing density-driven pattern formation in an essentially unmixed chemical system: the reaction of pale yellow Fe3+ with colorless SCN− to form the blood-red Fe(SCN)2+ complex ion in aqueous solution. Careful addition of one drop of Fe(NO3)3 to KSCN yields striped patterns after several minutes. The patterns appear reminiscent of Rayleigh-Taylor instabilities and convection rolls, arguing that pattern formation is caused by density-driven mixing.

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Experimental Evidence of Marangoni Convection Rolls in Belousov-Zhabotinsky Reaction

Complexity and Diversity ◽

10.1007/978-4-431-66862-6_27 ◽

1997 ◽

pp. 135-137

Author(s):

Osamu Inomoto ◽

Akemi Sakaguchi ◽

Shoichi Kai

Keyword(s):

Experimental Evidence ◽

Marangoni Convection ◽

Convection Rolls ◽

Belousov Zhabotinsky Reaction

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The Rayleigh–Bénard problem in intermediate bounded domains

Journal of Fluid Mechanics ◽

10.1017/s0022112093002186 ◽

1993 ◽

Vol 254 ◽

pp. 375-400 ◽

Cited By ~ 20

Author(s):

F. Stella ◽

G. Guj ◽

E. Leonardi

Keyword(s):

Flow Pattern ◽

Quantitative Comparison ◽

Flow Structures ◽

Bounded Domains ◽

Oscillatory Regime ◽

Rectangular Container ◽

Two Dimensional Flow ◽

Convection Rolls ◽

Rayleigh Benard Convection ◽

Rayleigh Benard

The stationary instabilities of flow patterns associated with Rayleigh–Bénard convection in a 3 × 1 × 9 rectangular container are extensively investigated by numerical simulation. Two types of spatial instabilities of the base convection rolls are predicted in the transition from steady two-dimensional flow to the unsteady oscillatory regime; these instabilities depend on the Prandtl number. For Pr = 0.71 the soft-roll instability is found at moderate Rayleigh number Ra. The results obtained confirm the importance of this flow pattern as a continuous mechanism for steady transition from one wavenumber to another. For Pr = 15, cross-roll instability is obtained, which at larger Ra leads to bimodal convection. For this value of Pr the soft-roll flow pattern is found at intermediate Ra. At higher Ra a new flow structure in which cross-rolls are superimposed on the soft roll is obtained. The effects of the various flow structures on the heat transfer are given. A quantitative comparison with previous experimental and theoretical findings is also presented and discussed.

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Instability of rotating convection

Journal of Fluid Mechanics ◽

10.1017/s0022112099006941 ◽

2000 ◽

Vol 403 ◽

pp. 153-172 ◽

Cited By ~ 28

Author(s):

S. M. COX ◽

P. C. MATTHEWS

Keyword(s):

Small Angle ◽

Large Scale ◽

Resonant Mode ◽

Heteroclinic Cycle ◽

Mean Flow ◽

Full Account ◽

Rapid Rotation ◽

Critical Wavelength ◽

Mode Interactions ◽

Convection Rolls

Convection rolls in a rotating layer can become unstable to the Küppers–Lortz instability. When the horizontal boundaries are stress free and the Prandtl number is finite, this instability diverges in the limit where the perturbation rolls make a small angle with the original rolls. This divergence is resolved by taking full account of the resonant mode interactions that occur in this limit: it is necessary to include two roll modes and a large-scale mean flow in the perturbation. It is found that rolls of critical wavelength whose amplitude is of order ε are always unstable to rolls oriented at an angle of order ε2/5. However, these rolls are unstable to perturbations at an infinitesimal angle if the Taylor number is greater than 4π4. Unlike the Küppers–Lortz instability, this new instability at infinitesimal angles does not depend on the direction of rotation; it is driven by the flow along the axes of the rolls. It is this instability that dominates in the limit of rapid rotation. Numerical simulations confirm the analytical results and indicate that the instability is subcritical, leading to an attracting heteroclinic cycle. We show that the small-angle instability grows more rapidly than the skew-varicose instability.

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Spatio-temporal patterns in inclined layer convection

Journal of Fluid Mechanics ◽

10.1017/jfm.2016.186 ◽

2016 ◽

Vol 794 ◽

pp. 719-745 ◽

Cited By ~ 11

Author(s):

Priya Subramanian ◽

Oliver Brausch ◽

Karen E. Daniels ◽

Eberhard Bodenschatz ◽

Tobias M. Schneider ◽

...

Keyword(s):

Boussinesq Equations ◽

Temporal Patterns ◽

Resonant Interaction ◽

Onset Of Convection ◽

Inclined Layer ◽

Spatio Temporal ◽

The Rich ◽

Convection Patterns ◽

Oriented Parallel ◽

Convection Rolls

This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle ${\it\gamma}$ and the Rayleigh number $R$. The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck–Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy driven and shear-flow driven pattern forming mechanisms. The former are expressed as longitudinal convection rolls with their axes oriented parallel to the incline, the latter as perpendicular transverse rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3-D convection patterns above onset of convection in the ${\it\gamma}{-}R$ plane, and find that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies.

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