POF Nameplate
  • Volume/Page
  • Keyword
  • DOI
  • Citation
  • Advanced
   
 
 
 

Flickr Twitter iResearch App Facebook

Search Issue | RSS Feeds RSS
Previous Issue Next Issue

Jun 2012

Volume 24, Issue 6, Articles (06xxxx)

Issue Cover Spotlight Figure

Phys. Fluids 24, 063302 (2012); http://dx.doi.org/10.1063/1.4729453 (18 pages)

Wenbo Tang, Brent Knutson, Alex Mahalov, and Reneta Dimitrova
Enlarge Image | Read More
Return to All Sections
back to top
RSS Feeds
back to top Instability and Transition

Numerical study of the onset of thermosolutal convection in rotating spherical shells

Marta Net, Ferran Garcia, and Juan Sánchez

Phys. Fluids 24, 064101 (2012); http://dx.doi.org/10.1063/1.4723865 (21 pages) | Cited 1 time

Online Publication Date: 1 June 2012

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The influence of an externally enforced compositional gradient on the onset of convection of a mixture of two components in a rotating fluid spherical shell is studied for Ekman numbers E = 10−3 and E = 10−6, Prandtl numbers σ = 0.1, 0.001, Lewis numbers τ = 0.01, 0.1, 0.8, and radius ratio η = 0.35. The Boussinesq approximation of the governing equations is derived by taking the denser component of the mixture for the equation of the concentration. Differential and internal heating, an external compositional gradient, and the Soret and Dufour effects are included in the model. By neglecting these two last effects, and by considering only differential heating, it is found that the critical thermal Rayleigh number Rec depends strongly on the direction of the compositional gradient. The results are compared with those obtained previously for pure fluids of the same σ. The influence of the mixture becomes significant when the compositional Rayleigh number Rc is at least of the same order of magnitude as the known Rec computed without mixture. For positive and sufficiently large compositional gradients, Rec decreases and changes sign, indicating that the compositional convection becomes the main source of instability. Then the critical wave number mc decreases, and the drifting waves slow down drastically giving rise to an almost stationary pattern of convection. Negative gradients delay the onset of convection and determine a substantial increase of mc and ωc for Rc sufficiently high. Potential laws are obtained numerically from the dependence of Rec and of the critical frequency ωc on Rc, for the moderate and small Ekman numbers explored.
Show PACS
47.55.pb Thermal convection
47.27.te Turbulent convective heat transfer
47.27.tb Turbulent diffusion
47.32.Ef Rotating and swirling flows
47.35.-i Hydrodynamic waves

The onset of steady vortices in Taylor-Couette flow: The role of approximate symmetry

K. A. Cliffe, T. Mullin, and D. Schaeffer

Phys. Fluids 24, 064102 (2012); http://dx.doi.org/10.1063/1.4726252 (18 pages)

Online Publication Date: 8 June 2012

Full Text: Read Online (HTML) | Download PDF

Show Abstract
The onset of steady cellular motion in Taylor-Couette flow between a pair of finite length cylinders is studied. This is most often portrayed in the literature as an example of a simple pitchfork bifurcation where the trivial state of rotary Couette flow is replaced by cellular motion above a critical Reynolds number. However, numerous experiments and simulations of the Navier-Stokes equations, as well as the detailed numerical bifurcation study reported here, all lead to the following, seemingly paradoxical, conclusion: On the one hand, no matter how long the apparatus, finite-length effects greatly perturb the disconnected branch of the pitchfork of the periodic model. This corresponds to anomalous-mode flows which are observed to exist above a range of Reynolds number that is at least a factor of two greater than the value corresponding to the onset of cells. On the other hand, in long cylinders these effects appear to change the connected branch of normal-mode flows only minimally. We propose a resolution of this paradox in terms of a symmetry breaking bifurcation. The relevant symmetry, which is only approximate, is between two normal-mode flows with large, and nearly equal, numbers of cells. Additionally, our numerical calculations establish a scaling law that quantifies the magnitude of finite-length effects on normal-mode flows at large lengths.
Show PACS
47.32.C- Vortex dynamics
47.15.Fe Stability of laminar flows
47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
47.11.-j Computational methods in fluid dynamics
47.10.ad Navier-Stokes equations
Return to All Sections
Close

Google Calendar

ADVERTISEMENT

Go to AIP Home   © AIP Publishing LLC
close