Axisymmetric and non-axisymmetric convection in a cylindrical container

Kirchartz, K. R.; Müller, Ulrich; Oertel, Herbert; Zierep, Jürgen

doi:10.1007/bf01170430

Cited by 31 publications

(6 citation statements)

References 14 publications

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“…After several days the annulus pattern is completely destroyed leading to a structure similar to a natural one. Such an instability of axisymmetric structures has already been observed by Stork and Muller [13] and more recently by K. R. Kirkchatz, et al [14]. This Tesult is also in agreement with the prediction of M. C. Cross [ 15].…”

supporting

confidence: 90%

“…a) corresponds to s = -0.069, b) to 8 = -0.036, c) to e = 0.004, d) to e = 0.023, d) to e = 0.040, f) to s = 0.077, g) toe = 0.111 l (100 Hz H 30 gm/s). K. R. Kirkchartz et ale in a cylindrical container [14] correspond to a case which is closer to perfectly conducting sidewalls than ours since their glass sidewall is likely to have a conductivity about 8 times higher than that of their fluid K. R. Kirkwharts et al also found that the axisymmetric structure was unstable when they applied a steady temperature gradient but they observed that the structure is in fact made up of well-aligned rolls. In their case the rolls do not seem to bend in order to end perpendicularly to the sidewalls.…”

mentioning

confidence: 51%

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Rayleigh-Bénard convective structures in a cylindrical container

Croquette¹,

Mory²,

Schosseler³

1983

J. Phys. France

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2014 Dans cet article nous faisons une étude des différentes structures convectives que l'on peut observer dans une géométrie cylindrique telle que le diamètre soit égal à 20 fois la hauteur. Pour un nombre de Prandtl de 380, ces structures apparaissent désordonnées mais stationnaires (après une phase de relaxation). Nous montrons que ces structures désordonnées sont plus stables que les solutions axisymétriques et nous indiquons comment les conditions aux limites jouent un rôle essentiel sur la stabilité de ces dernières. Enfin, nous considérons deux types de défauts, que l'on rencontre fréquemment dans les structures désordonnées. Nous les étudions par l'intermédiaire de leur champ de vitesse obtenu par vélocimétrie laser. Nous montrons que cette méthode nous permet une comparaison quantitative avec des théories récentes.

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supporting

confidence: 90%

mentioning

confidence: 51%

Rayleigh-Bénard convective structures in a cylindrical container

Croquette¹,

Mory²,

Schosseler³

1983

J. Phys. France

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“…The existence of several different stable convective flow patterns under the same external conditions has been nicely documented by Kirchartz et al (1981) for the case of a cylindrical cell of diameter-to-height ratio 6. They used a novel technique based on differential optical interferometry to determine three-dimensional density profiles, and showed that either axisymmetric or non-axisymmetric flows can be obtained, depending on the rate of change of R. Because our rectangular cell is much larger and does not have rotational symmetry, it seems reasonable to expect a much greater variety of flow patterns than they found.…”

Section: Stable Flows In Jinite Geometriesmentioning

confidence: 79%

Convective pattern evolution and secondary instabilities

1982

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Using an automated laser-Doppler scanning technique, we have performed an extensive study of pattern evolution and instabilities in a large Rayleigh-BBnard cell (20 by 30 times the layer depth) at moderate Prandtl number (2.5). This work differs from earlier experiments in that the Doppler mapping technique permits both the spatial structure and time evolution of the velocity field to be quantitatively studied, and runs lasting up to ten thousand vertical thermal diffusion times are presented. We observe and document the properties of three qualitatively different regimes above the critical Rayeigh number Rc. (i) Below 5Rc, there are a number of simple patterns in which the rolls align perpendicular to all lateral cell boundaries. The patterns are therefore curved and generally contain two boundary-related defects. A change in R induces patterns with many defects, which evolve toward the simple patterns over extraordinarily long times. These features seem to be consistent with theoretical models based on the competition between boundary, curvature and defect contributions to a Liapunov functional. However, stable states are not always reached. (ii) Above 5Rc the skewed-varicose instability of Busse & Clever causes progressively faster broadband time dependence with a spectral tail falling off approximately as the fourth power of the frequency. Doppler imaging shows that the fluctuations are caused by narrowing and pinching off of the rolls. (iii) Above 9Rc both the oscillatory and skewed-varicose instabilities cause local velocity fluctuations. However, substantial mean roll structure persists even over a 40 h period (one horizontal thermal diffusion time) at 1 5Rc. Velocity power spectra with two distinct maxima associated with the two instabilities are still resolved at 50Rc. Finally, we impose thermal inhomogeneities in order to pin the rolls, and show that the fluctuations are suppressed only if the local heat flux is a significant fraction of the convective heat transport per wavelength.

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“…Also, Cross (1982) has concluded that parallel rolls will be preferred over axisymmetric rolls in a cylindrical container. In this regard, experiments in cylindrical containers by Stork & Muller (1974, Kirchartz et al (1981 Heutmaker, Fraenkel & Gollub (1985) and Pocheau, Croquette & Le Gal (1985) show non-axisymmetric roll patterns in cylindrical containers in the absence of strong perturbations a t the sidewalls to enforce the axisymmetry. I n particular, Pocheau et al (1985) find nearly parallel rolls for R close to R, in an experiment using argon gas (Pr = 0.69) in a cylindrical container with r = 7.66.…”

Section: Introductionmentioning

confidence: 98%

Heat-flow experiments in liquid ⁴He with a variable cylindrical geometry

Metcalfe

Jung

et al. 1987

J. Fluid Mech.

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This paper first describes an apparatus for measuring the Nusselt number N versus the Rayleigh number R of convecting normal liquid 4He layers. The most important feature of the apparatus is its ability to provide layers of different heights d, and hence different aspect ratios [Gcy ]. The horizontal cross-section of each layer is circular, and [Gcy ] is defined by [Gcy ] = D/2d where D is the diameter of the layer. We report results for 2.4 [les ] [Gcy ] [les ] 16 and for Prandtl numbers Pr spanning 0.5 [lsim ] Pr [lsim ] 0.9 These results are presented in terms of the slope N1 = RcdN/dR evaluated just above the onset of convection at Rc. We find that N1 is only a slowly increasing function of [Gcy ] in the range 6 [lsim ] [Gcy ] [lsim ] 16, and that it has a value there which is quite close to 0.72. This value of N1 is in good agreement with variational calcuations by Ahlers et al. (1981) pertinent to parallel convection rolls in cylindrical geometry. Particularly for [Gcy ] [lsim ] 6, we find additional small-scale structure in N1 associated with changes in the number of convection rolls with changing [Gcy ]. An additional test of the linearzied hydrodynamics is given by measurements of Rc. We find good agreement between theory and our data for Rc.

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Axisymmetric and non-axisymmetric convection in a cylindrical container

Cited by 31 publications

References 14 publications

Rayleigh-Bénard convective structures in a cylindrical container

Rayleigh-Bénard convective structures in a cylindrical container

Convective pattern evolution and secondary instabilities

Heat-flow experiments in liquid ⁴He with a variable cylindrical geometry

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Axisymmetric and non-axisymmetric convection in a cylindrical container

Cited by 31 publications

References 14 publications

Rayleigh-Bénard convective structures in a cylindrical container

Rayleigh-Bénard convective structures in a cylindrical container

Convective pattern evolution and secondary instabilities

Heat-flow experiments in liquid 4He with a variable cylindrical geometry

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Heat-flow experiments in liquid ⁴He with a variable cylindrical geometry