Traveling-wave wall states in rotating Rayleigh-Bénard convection

Kuo, E. Y.; Mc, Cross

doi:10.1103/physreve.47.r2245

Cited by 71 publications

(70 citation statements)

References 7 publications

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“…The coefficients τ 0 , s d , c 0 , ξ 2 0 , c 1 , g 0 and c 3 can in principle be calculated from the underlying equations of motion [15,35,36]. For many experimental situations, however, such calculations are not available or can only be done in certain approximations; for some systems the equations of motion or boundary conditions are not even known in enough detail to allow such calculations.…”

Section: A1 Measuring the Cgle Coefficientsmentioning

confidence: 99%

Coherent and incoherent structures in systems described by the 1D CGLE: experiments and identification

Hecke¹

2003

Physica D: Nonlinear Phenomena

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Much of the nontrivial dynamics of the one dimensional Complex Ginzburg-Landau Equation (CGLE) is dominated by propagating structures that are characterized by local "twists" of the phase-field. I give a brief overview of the most important properties of these various structures, formulate a number of experimental challenges and address the question how such structures may be identified in experimental space-time data sets.

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Section: A1 Measuring the Cgle Coefficientsmentioning

confidence: 99%

Coherent and incoherent structures in systems described by the 1D CGLE: experiments and identification

Hecke¹

2003

Physica D: Nonlinear Phenomena

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“…Motivated by the wish to understand the fundamental dynamics taking place in planetary fluid interiors and atmospheres, convection in rotating cylindrical geometry has been extensively studied both experimentally and theoretically (see, for example, Daniels 1980;Zhong, Ecke & Steinberg 1991;Herrmann & Busse 1993;Kuo & Cross 1993;Aurnou et al 2003;Plaut 2003;Young & Read 2008). In particular, careful numerical studies of convective instabilities in a fluid contained in a circular cylinder uniformly heated from below and rotating about its vertical axis (Goldstein et al 1993(Goldstein et al , 1994 reveal an exceedingly complicated and seemingly incomprehensible behaviour at small and moderate Prandtl numbers.…”

Section: Introductionmentioning

confidence: 99%

The onset of convection in rotating circular cylinders with experimental boundary conditions

Zhang

Liao

2009

J. Fluid Mech.

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Convective instabilities in a fluid-filled circular cylinder heated from below and rotating about its vertical axis are investigated both analytically and numerically under experimental boundary conditions. It is found that there exist two different forms of convective instabilities: convection-driven inertial waves for small and moderate Prandtl numbers and wall-localized travelling waves for large Prandtl numbers. Asymptotic solutions for both forms of convection are derived and numerical simulations for the same problem are also performed, showing a satisfactory quantitative agreement between the asymptotic and numerical analyses.

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“…The first is when ⌫T 1/6 1. In this case, convection is in the form of a wall-localized travelling wave ͑for example, Davies-Jones and Gilman, 3 Zhong et al, 9 Goldstein et al, 10 Herrmann and Busse, 11 Kuo and Cross, 12 Liao et al 6 ͒. In contrast to the Hele-Shaw-type flow, the wall-localized convection is oscillatory and concentrates only in the vicinity of the vertical sidewalls.…”

Section: Introductionmentioning

confidence: 92%

Convective instabilities in a rotating vertical Hele-Shaw cell

et al. 2006

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Convective instabilities driven by vertical buoyancy in a Boussinesq fluid in a rotating vertical Hele-Shaw cell, a long channel with rectangular cross section of finite height h and small width ⌫h with ⌫ 1, are investigated both analytically and numerically. The problem is characterized by the Taylor number T, the Rayleigh number R, and the aspect ratio ⌫. Explicit asymptotic solutions describing convective instabilities are derived for ⌫T 1/6 1, where T is assumed to be large compared to unity. Comparison between the asymptotic and fully numerical solutions shows a satisfactory quantitative agreement. It is found that an overall condition for convective instabilities becomes optimal when ⌫T 1/6 = O͑1͒. Direct three-dimensional simulations for strongly nonlinear convection are also carried out in the regime 0 Ͻ ͑R − R c ͒ / R c Յ O͑10͒, where R c denotes the critical Rayleigh number. As a consequence of both the geometric and dynamic constraints imposed by the narrow channel ͑geometric͒ and rapid rotation ͑dynamic͒, the nonlinear flow remains temporally stationary and spatially simple and is comprised primarily of vertically long thin convection cells that transport heat all the way from the bottom to the top of the channel.

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Traveling-wave wall states in rotating Rayleigh-Bénard convection

Cited by 71 publications

References 7 publications

Coherent and incoherent structures in systems described by the 1D CGLE: experiments and identification

Coherent and incoherent structures in systems described by the 1D CGLE: experiments and identification

The onset of convection in rotating circular cylinders with experimental boundary conditions

Convective instabilities in a rotating vertical Hele-Shaw cell

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