Horizontal Wave Number Dependence of Type II Solutions in Rayleigh?Benard Convection with Hexagonal Planform

Lopez, JM; Murphy, J. O.

doi:10.1071/ph840531

Cited by 3 publications

(5 citation statements)

References 4 publications

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“…now assume and introduce both these expressions into equation 2which, after the elimination of exp(pt), leads to The numerical results for p, when a = 1, are given in (R -a) parameter space in Figure 3. The zero level contour in this diagram is the demarcation line which separates the type I and type II solutions and is in excellent agreement with the type of solution obtained independently from the time integrations of equations (1) -(4) (Lopez and Murphy 1983). Moreover, the location of this contour confirms that type II solutions cannot become established in narrow cells where the closeness of the side walls would inhibit the characteristic swirling motions.…”

Section: Z{zt)=y(z)exp[pl)supporting

confidence: 84%

“…The convective model for the Boussinesq fluid layer is based on the following single-mode equations and associated parameters (Lopez and Murphy 1983):…”

Section: Basic Equationsmentioning

confidence: 99%

“…Overall the time dependence of N, Figure 6, follows that of W(z,t) and a feature of particular physical interest is the resultant drop in the convective heat transport which occurs following the growth of Z (z,t). It is also astrophysically significant that these solutions only exist when the Prandtl number is small and for convection cells with small horizontal wave numbers and hence smaller aspect ratio (Lopez and Murphy 1984).…”

Section: Z{zt)=y(z)exp[pl)mentioning

confidence: 99%

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A Nonlinear Bifurcation in Cellular Convection Theory

Yannios

Lopez

Murphy

1986

Publ. Astron. Soc. Aust.

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Time dependent solutions of the nonlinear modal equations for cellular convection in a fluid layer heated below have demonstrated the existence of a nonlinear bifurcation which leads to a stable regime with reduced heat flux and vertical velocities. This new state is brought about by the growth, to a significant level, of the vertical component of vorticity after an initial quasi-steady state has been established. The growth rate mechanism has been investigated analytically and compared with the numerical results. These vorticity modified solutions exhibit favourable features Which could be established in the solar convection zone.

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Section: Z{zt)=y(z)exp[pl)supporting

confidence: 84%

“…The convective model for the Boussinesq fluid layer is based on the following single-mode equations and associated parameters (Lopez and Murphy 1983):…”

Section: Basic Equationsmentioning

confidence: 99%

Section: Z{zt)=y(z)exp[pl)mentioning

confidence: 99%

See 1 more Smart Citation

A Nonlinear Bifurcation in Cellular Convection Theory

Yannios

Lopez

Murphy

1986

Publ. Astron. Soc. Aust.

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“…Numerical simulations showing vertical vortices in a pure convecting layer include the large-eddy simulations of Mason (1989) and Kanak et al (2000). In those simulations, the no-slip lower boundary was a possible source of vorticity for the vortices.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh‐Bénard convection as a tool for studying dust devils

Fiedler

Kanak

2001

Atmospheric Science Letters

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Intense columnar vortices in a convecting layer are explored with direct numerical simulations that are otherwise similar to the large-eddy simulations of Kanak et al. (2000. With free-slip boundaries and a Rayleigh number of 10 6 (4096 times critical), vortices similar to large dust devils are readily produced. The genesis, intensity and life cycle of these intense vortices (dust devils) are studied. The simulated dust devils last for the order of the over-turning time of the largest eddies. The intensity is limited by the hydrostatic pressure drop supported by the buoyancy con®ned in the core. The genesis of a simulated dust devil requires not only tilting of the baroclinically generated vorticity, but also a symmetry-breaking event that allows one sign of vorticity to become concentrated in an updraft. Such symmetry breaking is the rule with random initialization in the simulations. However, when initialization is restricted to certain Fourier modes, exceptions are found that produce only symmetric vortex couplets that are relatively weak.*

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“…The modal équations governing convection within hexagonal cells hâve, in addition to the planform interaction constant, a dependence on the Prandtl number a. It has been shown (Lopez and Murphy 1984) that the inclusion of this ratio of the viscous to thermal djffusivities has a substantial effect on the variation of a for maximum N and W mix . When R = 10 4 , a ma x oe 3.02 for Afmax at (7=0.5 ( Figure 4) compared with ««2.89 for N max computed from the mean field équations for steady convection.…”

Section: W"mentioning

confidence: 99%

Preferred Horizontal Scale for Thermal Convection

Fiedler¹,

Murphy²

1986

Publ. Astron. Soc. Aust.

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Linear stability theory for Rayleigh-Benard convection shows that for a specified Rayleigh number, greater than some critical value, only a finite range of horizontal wave numbers support convective instability in a horizontal layer of fluid heated from below. However, it is not possible to predict the preferred horizontal scale of established motions from this approach although it is clear from observations, particularly of the solar surface, that a preferred cell size does prevail. In an endeavour to establish a preferred horizontal scale appropriate non-linear modal equations have been integrated forward in time, initially incorporating a discrete band of wave numbers equally spaced across the range that supports convection, for a specific Rayleigh number. The horizontal resolution was improved in subsequent integrations by first deleting modes that had substantially decayed and then introducing new modes on a finer horizontal mesh in the vicinity of what appeared to be the evolutionary dominant mode. Finally, the multimode integrations were continued in time until the evolution of a dominant horizontal mode from within the restricted range was evident. Both the model characteristics and numerical scheme adopted placed limits on the degree of horizontal refinement that could be undertaken with confidence.

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Horizontal Wave Number Dependence of Type II Solutions in Rayleigh?Benard Convection with Hexagonal Planform

Cited by 3 publications

References 4 publications

A Nonlinear Bifurcation in Cellular Convection Theory

A Nonlinear Bifurcation in Cellular Convection Theory

Rayleigh‐Bénard convection as a tool for studying dust devils

Preferred Horizontal Scale for Thermal Convection

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