Rayleigh-Bénard convection with rotation at small Prandtl numbers

Bajaj, Kapil M. S.; Ahlers, Guenter; Pesch, Werner

doi:10.1103/physreve.65.056309

Cited by 36 publications

(43 citation statements)

References 41 publications

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“…This physical configuration has been studied for the wealth of instabilities it exhibits 3,20,21 and for the small amplitude but complex dynamics that result. [22][23][24] We restrict attention to two-dimensional convection described by the dimensionless equations, written in the rotating frame,…”

Section: Introductionmentioning

confidence: 99%

Localized rotating convection with no-slip boundary conditions

et al. 2013

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Localized patches of stationary convection embedded in a background conduction state are called convectons. Multiple states of this type have recently been found in two-dimensional Boussinesq convection in a horizontal fluid layer with stress-free boundary conditions at top and bottom, and rotating about the vertical. The convectons differ in their lengths and in the strength of the self-generated shear within which they are embedded, and exhibit slanted snaking. We use homotopic continuation of the boundary conditions to show that similar structures exist in the presence of no-slip boundary conditions at the top and bottom of the layer and show that such structures exhibit standard snaking. The homotopic continuation allows us to study the transformation from slanted snaking characteristic of systems with a conserved quantity, here the zonal momentum, to standard snaking characteristic of systems with no conserved quantity. C 2013 AIP Publishing LLC. [http://dx

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Section: Introductionmentioning

confidence: 99%

Localized rotating convection with no-slip boundary conditions

et al. 2013

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“…The bursts changed the flow direction randomly. The phenomenon of bursting was also observed in a lowPrandt-number Rayleigh-Bénard experiment in presence of a uniform rotation 16 . The flow direction was not found to flip in this experiment.…”

Section: A Fluid Patterns With a Vertical Magnetic Fieldmentioning

confidence: 63%

“…A homoclinic bifurcation may lead to the possibility of Shilnikov wiggle 11 , three-frequency quasi-periodic orbits 12,13 , spontaneous gluing of two limit cycles into a large one or spontaneous breaking of a limit cycle into two smaller ones 2,4-6 or homoclinic chaos. This may also lead to the phenomenon of pattern bursting [14][15][16][17] , when a fluid pattern disappears for a finite time and reappears again for a fixed value of the bifurcation parameter.…”

Section: Introductionmentioning

confidence: 99%

Effects of a small magnetic field on homoclinic bifurcations in a low-Prandtl-number fluid

Basak

Kumar

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-Bénard convection in a fluid of Prandtl number P r = 0.01 are investigated using direct numerical simulations (DNS). A uniform magnetic field is applied either in the vertical or in the horizontal direction. For a weak vertical magnetic field, the possibilities of both forward and backward homoclinic bifurcations are observed leading to a spontaneous merging of two limit cycles into one as well as a spontaneous breaking of a limit cycle into two for lower values of the Chandrasekhar's number (Q ≤ 5). A slightly stronger magnetic field makes the convective flow time independent giving the possibility of stationary patterns at the secondary instability. For horizontal magnetic field, the x ⇌ y symmetry is destroyed and neither a homoclinic gluing nor a homoclinic breaking is observed. Two low-dimensional models are also constructed: one for a weak vertical magnetic field and another for a weak horizontal magnetic field. The models qualitatively capture the features observed in DNS and help understanding the unfolding of bifurcations close to the onset of magnetoconvection. Dissipative structures spontaneously appear in several continuum mechanical systems when they are subjected to a uniform external forcing. The dynamics of such structures depends upon the nature of the underlying bifurcations. A dynamical system having symmetrically placed saddle and unstable fixed points in its phase space may show the possibility of either homoclinic or heteroclinic bifurcations. Several fluid dynamical systems show homoclinic gluing of two limit cycles into one. This may lead to the phenomenon of pattern bursting, where a dissipative structure disappears for a finite time and then reappears again for a fixed value of the bifurcation parameter. Fluid patterns in Rayleigh-Bénard convection in low-Prandtl-number fluids with stress-free boundaries show homoclinic as well as heteroclinic dynamics. A uniform applied magnetic field produces Lorentz force which is likely to affect this behavior significantly. The role of a small magnetic field on such behavior is not known. Direct numerical simulations and low-dimensional models for magnetoconvection show that a small vertical magnetic field allows homoclinic gluing. However, even a very weak horizontal magnetic field destroys homoclinic gluing, as it breaks the rotational symmetry of the flow structure about a vertical axis. The unfolding of bifurcations near the instability onset is quite different for a vertical magnetic field from that for a horizontal magnetic field.

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“…In comparison to numerous studies of RC in moderate Prandtl number fluids [11,13,14,20,23,[63][64][65][66][67][68][69][70], only a rather limited number of rotating convection investigations have been made in low Prandtl number fluids [18][19][20]51,71]. The governing equations for rotating convection are i.e., the angular velocity Ω = 0.84 rad/s and the rotation period P Ω = 7.5 s. The height of the layer is fixed at H = 10 cm.…”

Section: Essential Theorymentioning

confidence: 99%

Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals

Ribeiro¹,

Fabre²,

Guermond³

et al. 2015

Metals

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Planets and stars are often capable of generating their own magnetic fields. This occurs through dynamo processes occurring via turbulent convective stirring of their respective molten metal-rich cores and plasma-based convection zones. Present-day numerical models of planetary and stellar dynamo action are not carried out using fluids properties that mimic the essential properties of liquid metals and plasmas (e.g., using fluids with thermal Prandtl numbers P r < 1 and magnetic Prandtl numbers P m 1). Metal dynamo simulations should become possible, though, within the next decade. In order then to understand the turbulent convection phenomena occurring in geophysical or astrophysical fluids and next-generation numerical models thereof, we present here canonical, end-member examples of thermally-driven convection in liquid gallium, first with no magnetic field or rotation present, then with the inclusion of a background magnetic field and then in a rotating system (without an imposed magnetic field). In doing so, we demonstrate the essential behaviors of convecting liquid metals that are necessary for building, as well as benchmarking, accurate, robust models of magnetohydrodynamic processes in P m P r < 1 geophysical and astrophysical systems. Our study results also show strong agreement between laboratory and numerical experiments, demonstrating that high resolution numerical simulations can be made capable of modeling the liquid metal convective turbulence needed in accurate next-generation dynamo models.

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Rayleigh-Bénard convection with rotation at small Prandtl numbers

Cited by 36 publications

References 41 publications

Localized rotating convection with no-slip boundary conditions

Localized rotating convection with no-slip boundary conditions

Effects of a small magnetic field on homoclinic bifurcations in a low-Prandtl-number fluid

Canonical Models of Geophysical and Astrophysical Flows: Turbulent Convection Experiments in Liquid Metals

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