Effect of rotation on the stability of a bounded cylindrical layer of fluid heated from below

Buell, Jeffrey C.

doi:10.1063/1.864238

Cited by 48 publications

(28 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We find that the first bifurcation is a Hopf bifurcation to a time-periodic state in which the convective structure precesses in the rotating frame. The spatial symmetry of our pattern agrees qualitatively with a recent linear-stability analysis [3]; but in the theoretical work it was assumed that the structure would be stationary in the rotating frame. An interesting aspect of this instability in the finite system, noticed also in previous heat transport experiments [4,5], is that it occurs at a smaller value of A7" than the predicted value for the infinite system.…”

supporting

confidence: 87%

Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection

1991

View full text Add to dashboard Cite

We report heat transport measurements and optical shadowgraph visualization of rotating Rayleigh-Benard convection. For dimensionless rotation rates 140 < Ct < 4300, the initial transition to convection, occurring at a Rayleigh number R much less than the linear-stability value for roll or vortex states, is a forward Hopf bifurcation to an azimuthally asymmetric state with mode number n. States with n =3, 4, 5, 6, and 7 exist at low to moderate R and precess with frequencies that depend on R and ft. At higher R there is a continuous transition to a state with noisy, time-dependent heat transport, a distinct array of vortices in the central region, and a modulation of the precession speed of the outer structures. 47.25.Ae The combination of thermally induced buoyancy and of a Coriolis force is fundamental to many problems in geophysical fluid dynamics, in astrophysics, and in the study of nonlinear instabilities involving multiple control parameters. An important question is how turbulent states evolve in these systems. Here we present experimental results for a horizontal layer of fluid heated from below and rotated about a vertical axis, which may be regarded as an idealization of the problems mentioned above. For this case, it is known that convection is suppressed by the rotation, and at large rotation rates heat is predicted to be transported by vortex structures rather than by convection rolls [1,2]. Our experimental results are based on shadowgraph flow visualization and heat transport measurements for a cylindrical sample of radius-to-height ratio r = l. As the temperature difference AT is increased quasistatically, the measurements show that for ft =2145 the conductive state loses stability to a mode of fivefold azimuthal symmetry with amplitude maxima localized near the lateral wall. Modes with fourfold, fivefold, and sevenfold symmetry can also be created by using different time histories of AT. We find that the first bifurcation is a Hopf bifurcation to a time-periodic state in which the convective structure precesses in the rotating frame. The spatial symmetry of our pattern agrees qualitatively with a recent linear-stability analysis [3]; but in the theoretical work it was assumed that the structure would be stationary in the rotating frame. An interesting aspect of this instability in the finite system, noticed also in previous heat transport experiments [4,5], is that it occurs at a smaller value of A7" than the predicted value for the infinite system. This contrasts with the usual situation, where finite-size effects stabilize the conduction state.As AT is increased well beyond the first bifurcation point AT C , we find that the maxima of the flow field, which close to onset were localized near the lateral walls, develop spiral arms that reach into the cell interior and, with increasing AT 7 , form vortices with an initial spatial arrangement which retains the rt-fold symmetry of the states close to onset. Upon further increase of AT, the vortex structure becomes aperiodically time dependent a...

show abstract

supporting

confidence: 87%

Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection

1991

View full text Add to dashboard Cite

show abstract

“…For b ¼ 1, the critical mode is the antisymmetric m ¼ 1 mode. Using linear stability analyses, Buell and Catton [11] found that Ra cr ¼ 471, while Touihri et al [15] found that Ra cr ¼ 462. Using a numerical time integration of the full three-dimensional Navier-Stokes and energy equations, Neumann [16] found that Ra cr ¼ 451.…”

Section: Resultsmentioning

confidence: 98%

“…In this case, the first instability as the temperature difference is increased involves the transition to a steady axisymmetric or nonaxisymmetric flow. If the cylinder is rotated about its vertical centerline, the base-state consists of a rigid body rotation with the cylinder and a linear temperature variation, with the initial transition to an axisymmetric or nonaxisymmetric flow which is steady in a reference frame rotating with the cylinder [11]. For a fixed, finite-length cylinder with a rotating magnetic field, the base-state consists of (1) the azimuthal velocity v h0 ðr; zÞ driven by the RMF, (2) a meridional circulation which consists of radial and axial velocity components and which is driven by the axial variation of the centrifugal force due to v h0 , and (3) a temperature which deviates from a linear variation due to the convective heat transfer associated with the basestate meridional circulation.…”

Section: Introductionmentioning

confidence: 99%

Rayleigh–Bénard instability in a vertical cylinder with a rotating magnetic field

Walker

Volz

Mazuruk

2004

International Journal of Heat and Mass Transfer

View full text Add to dashboard Cite

“…18 In both papers, the thresholds for the mode k = 1 and large aspect ratios ͑height over radius͒ in which we are interested are given as critical curves from which it is difficult to extract precise data. But in another paper of Buell and Catton, 19 numerical data can be found that are given in Table III. These data can then be compared with the results of Rubinov et al 11 For A b =2 ͑heated from below͒, the critical Rayleigh number is Ra cr ͑A b =2͒ = 471.25, which agrees very well with Ra cr ͑A =5͒ = 473 ͑value extracted from Rubinov et al 11 ͒ for the case partially heated from the side.…”

Section: Comparison With the Case Heated From Below For Large Aspect mentioning

confidence: 96%

Three-dimensional numerical study of natural convection in vertical cylinders partially heated from the side

2005

View full text Add to dashboard Cite

Three-dimensional steady and oscillatory flows are simulated in a vertical cylinder partially heated from the side. The vertical wall is heated in a zone at midheight and is insulated above and below this middle zone, while both ends of the cylinder are cooled. The cylinder aspect ratio ͑A = height/ radius͒ ranges from 2 to 8, whereas a fixed Prandtl number, Pr= 0.021, is considered as well as a fixed length of the heated zone, equal to the cylinder radius. Three-dimensional steady and unsteady simulations as well as mode decomposition techniques and energy transfer analyses are used to characterize the flows and their transitions. The flows that develop from the steady toroidal pattern beyond the first instability threshold break the axisymmetry. At small A ͑2 ഛ A ഛ 2.5͒, the flow corresponds to a two-roll rotating pattern, which is triggered by a k = 2 azimuthal mode as a result of a hydrodynamic instability. At large A ͑3 ഛ A ഛ 8͒, the flow is steady and corresponds to a main one-roll pattern in the upper part of the cylinder. The flow is triggered by a k = 1 mode as a result of buoyancy effects affecting this unstably stratified upper part ͑Rayleigh-Bénard instability͒, but shear effects are involved in the instability for the smaller values of A. These steady flows then transit at a higher threshold to a standing-wave oscillatory one-roll pattern associated with the breaking of symmetry of the previous steady pattern. For intermediate values of A ͑2.7ഛ A ഛ 2.9͒, the transition is toward an oscillatory pattern, but hysteresis phenomena with multiplicity of steady and oscillatory states have been found. Comparisons with experiments performed at aspect ratios A = 4 and 8 are then considered and discussed.

show abstract

Effect of rotation on the stability of a bounded cylindrical layer of fluid heated from below

Cited by 48 publications

References 6 publications

Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection

Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection

Rayleigh–Bénard instability in a vertical cylinder with a rotating magnetic field

Three-dimensional numerical study of natural convection in vertical cylinders partially heated from the side

Contact Info

Product

Resources

About