Dynamics and Selection of Giant Spirals in Rayleigh-Bénard Convection

Plapp, Brendan B.; Egolf, David A.; Bodenschatz, Eberhard; Pesch, Werner

doi:10.1103/physrevlett.81.5334

Cited by 56 publications

(37 citation statements)

References 23 publications

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“…Some of them such as giant spirals or targets have been described already in experiments for the case of Rayleigh-Bénard convection with uniform heating. 2,4,5 Issues related to horizontal and vertical temperature differences have already been addressed in Refs. 14-16, but here we study for the first time the influence of the shape parameter ␤, which measures the width of the heating.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The first experimental observations on spirals 2,3 in Rayleigh-Bénard convection were rather surprising as they were carried out for a set of external parameter values in which parallel rolls should be stable. In experiments, spirals have been reported for finite Prandtl number 4 and both single-armed and multiarmed giant spirals, and spiral chaos, have been observed. In Ref.…”

Section: Introductionmentioning

confidence: 99%

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Instabilities in buoyant flows under localized heating

Navarro

Mancho

Herrero

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We study, from the numerical point of view, instabilities developed in a fluid layer with a free surface in a cylindrical container which is nonhomogeneously heated from below. In particular, we consider the case in which the applied heat is localized around the origin. An axisymmetric basic state appears as soon as a nonzero horizontal temperature gradient is imposed. The basic state may bifurcate to different solutions depending on vertical and lateral temperature gradients and on the shape of the heating function. We find different kinds of instabilities: extended patterns growing on the whole domain, which include those known as targets, and spiral waves. Spirals are present even for infinite Prandtl number. Localized structures both at the origin and at the outer part of the cylinder may appear either as Hopf or stationary bifurcations. An overview of the developed instabilities as functions of the dimensionless parameters is presented in this article. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2714295͔ Spiral and target wave instabilities in Rayleigh-Bérnard convection were experimentally found in the early 1990s and several theoretical mechanisms have been proposed to justify their appearance. In this article we study the instabilities generated in the flow by a nonuniform heating function. In this setup spiral and target waves are the linearly growing modes of nontrivial axisymmetric basic states. We find that localized structures also may appear. These patterns grow at different positions in the domain depending on the basic flow from which they bifurcate. This article reports a systematical numerical study of these transitions.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Instabilities in buoyant flows under localized heating

Navarro

Mancho

Herrero

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Although no studies have yet been published on such flows in porous media, it is well-known that such a variant of the classical Bénard problem may sometimes exhibit a rotating spiral convection pattern even though all the boundary conditions are steady and uniform; see Plapp et al (1998) [25].…”

Section: Palm Et Al (1972)mentioning

confidence: 99%

Horizontal Cellular Oscillations Caused by Time-Periodic Resonant Thermal Forcing in Weakly Nonlinear Darcy-Bénard Convection

Jais

Rees

2017

Fluids

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Abstract:The onset of Rayleigh-Bénard convection in a horizontally unbounded saturated porous medium is considered. Particular attention is given to the stability of weakly nonlinear convection between two plane horizontal surfaces heated from below. The primary aim is to study the effects on postcritical convection of having small amplitude time-periodic resonant thermal forcing. Amplitude equations are derived using a weakly nonlinear theory and they are solved in order to understand how the flow evolves with changes in the Darcy-Rayleigh number and the forcing frequency. When convection is stationary in space, it is found to consist of one of two different types depending on its location in parameter space: either a convection pattern where each cell rotates in the same way for all time with a periodic variation in amplitude (Type I) or a pattern where each cell changes direction twice within each forcing period (Type II). Asymptotic analyses are also performed (i) to understand the transition between convection of types I and II; (ii) for large oscillation frequencies and (iii) for small oscillation frequencies. In a large part of parameter space the preferred pattern of convection when the layer is unbounded horizontally is then shown to be one where the cells oscillate horizontally-this is a novel form of pattern selection for Darcy-Bénard convection.

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“…Spiral wave is one of the most typical two-dimensional spatiotemporal patterns in excitable media which has been observed and studied in many different biological [1][2][3][4], physical [5,6], chemical [7][8][9][10], and mathematical model systems [11,12]. In particular, spiral waves of excitation in heart tissue underlie certain types of dangerous cardiac arrhythmias such as ventricular tachycardias and fibrillation [13,14].…”

Section: Introductionmentioning

confidence: 99%

Motion of spiral waves induced by local pacing

Chen

Wei

et al. 2008

Open Physics

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Abstract:The motion of spiral waves in excitable media driven by a weak pacing around the spiral tip is investigated numerically as well as theoretically. We presented a Bifurcations diagram containing four types of the spiral motion induced by different frequencies of pacing: rigidly rotating, inward-petal meandering, resonant drift, and outward-petal meandering spiral. Simulation shows that the spiral resonantly drifts when the frequency of pacing is close to that of the spiral rotation. We also find that the speed and direction of the drift can be efficiently controlled by means of the strength and phase of the local pacing, which is consistent with analytical results based on the framework of the weak deformation approximation.

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Dynamics and Selection of Giant Spirals in Rayleigh-Bénard Convection

Cited by 56 publications

References 23 publications

Instabilities in buoyant flows under localized heating

Instabilities in buoyant flows under localized heating

Horizontal Cellular Oscillations Caused by Time-Periodic Resonant Thermal Forcing in Weakly Nonlinear Darcy-Bénard Convection

Motion of spiral waves induced by local pacing

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