Square Patterns in Rayleigh-Bénard Convection with Rotation about a Vertical Axis

Bajaj, Kapil M. S.; Liu, Jun; Naberhuis, Brian; Ahlers, Guenter

doi:10.1103/physrevlett.81.806

Cited by 46 publications

(42 citation statements)

References 29 publications

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“…The chiral symmetry breaking modifies the quadratic nonlinear terms through the coefficient a 2 , which is an odd function of T. The remaining spatial coefficients (£g> ct\ and (3) have to be even functions of T. We have derived spatial coefficients for the model equation (2) The linear correlation length £Q diminishes when T increases in qualitative agreement (though important differences still exist) with experimental findings in [Bajaj et al, 1998] (see Fig. 5).…”

Section: Wavenumber Perturbationssupporting

confidence: 72%

Hexagonal Patterns in a Model for Rotating Convection

Madruga

Pérez–García

2004

Int. J. Bifurcation Chaos

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We study a model equation that mimics convection under rotation in a fluid with temperaturedependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a Kiippers-Lortz instability [Kuppers & Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and oscillating hexagons quite well, and include the Busse-Heikes (BH) model [Busse & Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined.

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Section: Wavenumber Perturbationssupporting

confidence: 72%

Hexagonal Patterns in a Model for Rotating Convection

Madruga

Pérez–García

2004

Int. J. Bifurcation Chaos

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“…Experimental observations of spatially periodic square patterns have been reported in many different systems, for both small and large boxes. The most obvious examples include Rayleigh-Bénard convection (Oliver & Booker 1983), binary fluid convection (Moses & Steinberg 1991), rotating convection (Bajaj et al 1998), and Faraday surface wave experiments (Edwards & Fauve 1994). Hexagonal patterns are also widely observed.…”

Section: Discussionmentioning

confidence: 99%

Compressible magnetoconvection in three dimensions: pattern formation in a strongly stratified layer

et al. 2000

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ArticleThe interaction between magnetic fields and convection is interesting both because of its astrophysical importance and because the nonlinear Lorentz force leads to an especially rich variety of behaviour. We present several sets of computational results for magnetoconvection in a square box, with periodic lateral boundary conditions, that show transitions from steady convection with an ordered planform through a regime with intermittent bursts to complicated spatiotemporal behaviour. The constraints imposed by the square lattice are relaxed as the aspect ratio is increased. In wide boxes we find a new regime, in which regions with strong fields are separated from regions with vigorous convection. We show also how considerations of symmetry and associated group theory can be used to explain the nature of these transitions and the sequence in which the relevant bifurcations occur.

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“…Rayleigh-Bénard system rotating uniformly about a vertical axis [1][2][3][4][5][6][7][8][9] is an interesting problem for studying pattern-forming instabilities and bifurcations, [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] chaos, 26,27 and turbulence 28 in addition to its potential applications in rotating cryogenics. 31 The rotation about a vertical axis introduces Coriolis force as well as centrifugal force 32 in the flow.…”

Section: Introductionmentioning

confidence: 99%

Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

Pharasi¹,

Kumar²

2013

Physics of Fluids

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We present the results of direct numerical simulations of flow patterns in a lowPrandtl-number (P r = 0.1) fluid above the onset of oscillatory convection in a Rayleigh-Bénard system rotating uniformly about a vertical axis. Simulations were carried out in a periodic box with thermally conducting and stress-free top and bottom surfaces. We considered a rectangular box (L x ×L y ×1) and a wide range of Taylor numbers (750 ≤ T a ≤ 5000) for the purpose. The horizontal aspect ratio η = L y /L x of the box was varied from 0.5 to 10. The primary instability appeared in the form of two-dimensional standing waves for shorter boxes (0.5 ≤ η < 1 and 1 < η < 2).The flow patterns observed in boxes with η = 1 and η = 2 were different from those with η < 1 and 1 < η < 2. We observed a competition between two sets of mutually perpendicular rolls at the primary instability in a square cell (η = 1) for T a < 2700, but observed a set of parallel rolls in the form of standing waves for T a ≥ 2700. The three-dimensional convection was quasiperiodic or chaotic for 750 ≤ T a < 2700, and then bifurcated into a two-dimensional periodic flow for T a ≥ 2700. The convective structures consisted of the appearance and disappearance of straight rolls, rhombic patterns, and wavy rolls inclined at an angle φ = π 2 − arctan (η −1 ) with the straight rolls.

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Square Patterns in Rayleigh-Bénard Convection with Rotation about a Vertical Axis

Cited by 46 publications

References 29 publications

Hexagonal Patterns in a Model for Rotating Convection

Hexagonal Patterns in a Model for Rotating Convection

Compressible magnetoconvection in three dimensions: pattern formation in a strongly stratified layer

Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

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