Mixed-mode solutions in an air-filled differentially heated rotating annulus

Lewis, Gregory

doi:10.1016/j.physd.2010.05.004

Cited by 8 publications

(3 citation statements)

References 37 publications

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“…This study is devoted to an effect of destabilization of axisymmetric natural convection flows by a weak superimposed nonuniform rotation. In classical models, such as a rotating infinite layer (see, e.g., Chandrasekhar, 1961;Koschmieder,1993;Fernando & Smith IV, 2001;Kloosterziel & Carnevale, 2003;Lewis, 2010) or rotating cylinders and annuli (see, e.g., Lucas et al, 1983;Goldstein at al., 1993, Lopez & Marquez, 2009Rubio et al, 2010), increasing rotation usually leads to stabilization of the flow, i.e., to the growth of the critical Rayleigh number or other critical parameters describing magnitude of the buoyancy force. We do not review here numerous studies of the two above mentioned models, but address the reader to references in the cited papers.…”

Section: Introductionmentioning

confidence: 99%

Destabilization of free convection by weak rotation

Gelfgat

2011

J. Fluid Mech.

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This study offers an explanation of a recently observed effect of destabilization of free convective flows by weak rotation. After studying several models where flows are driven by a simultaneous action of convection and rotation, it is concluded that the destabilization is observed in the cases where centrifugal force acts against main convective circulation. At relatively low Prandtl numbers this counter action can split the main vortex into two counter rotating vortices, where the interaction leads to instability. At larger Prandtl numbers, the counter action of the centrifugal force steepens an unstable thermal stratification, which triggers Rayleigh-B\'enard instability mechanism. Both cases can be enhanced by advection of azimuthal velocity disturbances towards the axis, where they grow and excite perturbations of the radial velocity. The effect was studied considering a combined convective/rotating flow in a cylinder with a rotating lid and a parabolic temperature profile at the sidewall. Next, explanations of the destabilization effect for rotating magnetic field driven flow and melt flow in a Czochralski crystal growth model were derived

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Section: Introductionmentioning

confidence: 99%

Destabilization of free convection by weak rotation

Gelfgat

2011

J. Fluid Mech.

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“…The double-Hopf bifurcation has been reported in many works on fluid dynamical models. A few examples are baroclinic flows (Moroz and Holmes, 1984), rotating cylinder flows (Marqués et al, 2002(Marqués et al, , 2003, Poiseuille flows (Avila et al, 2006), rotating annulus flows (Lewis and Nagata, 2003;Lewis, 2010), and quasi-geostrophic flows (Lewis and Na- Figure 10. Continuation of periodic orbits for n = 40 and G = 0.…”

Section: Multi-stability: Coexistence Of Wavesmentioning

confidence: 99%

Wave propagation in the Lorenz-96 model

Kekem

Sterk

2018

Nonlin. Processes Geophys.

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Abstract. In this paper we study the spatiotemporal properties of waves in the Lorenz-96 model and their dependence on the dimension parameter n and the forcing parameter F. For F > 0 the first bifurcation is either a supercritical Hopf or a double-Hopf bifurcation and the periodic attractor born at these bifurcations represents a traveling wave. Its spatial wave number increases linearly with n, but its period tends to a finite limit as n → ∞. For F < 0 and odd n, the first bifurcation is again a supercritical Hopf bifurcation, but in this case the period of the traveling wave also grows linearly with n. For F < 0 and even n, however, a Hopf bifurcation is preceded by either one or two pitchfork bifurcations, where the number of the latter bifurcations depends on whether n has remainder 2 or 0 upon division by 4. This bifurcation sequence leads to stationary waves and their spatiotemporal properties also depend on the remainder after dividing n by 4. Finally, we explain how the double-Hopf bifurcation can generate two or more stable waves with different spatiotemporal properties that coexist for the same parameter values n and F.

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“…The double-Hopf bifurcation has been reported in many works on fluid dynamical models. A few examples are baroclinic flows (Moroz and Holmes, 1984), rotating cylinder flows (Marqués et al, 2002(Marqués et al, , 2003, Poiseuille flows (Avila et al, 2006), rotating annulus flows (Lewis and Nagata, 2003;Lewis, 2010), and quasi-geostrophic flows (Lewis and Na- Circles denote Neȋmark-Sacker bifurcations and triangles denote period doubling bifurcations. The Hopf bifurcations generating the waves with wave numbers 8, 9, and 7 occur at respectively F = 0.894, F = 0.902, and F = 0.959.…”

Section: Multi-stability: Coexistence Of Wavesmentioning

confidence: 99%