Wave dispersion in a rotating, differentially-heated fluid model

Lu, Huei-lin; Miller, Timothy L.

doi:10.1016/s0377-0265(97)00028-6

Cited by 3 publications

(2 citation statements)

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“…The radial, azimuthal and vertical (or axial) coordinates are denoted r, ϕ and z, respectively, with unit vectors e r , e ϕ and e z . This model is essentially the same as those used in many previous numerical studies, including, for example, [23,2,24,17,12]. With air as the working fluid, it is expected that the Boussinesq approximation will lead to quantitatively accurate results for ∆T < 50 [12], while above this, the results may only be qualitatively accurate.…”

Section: Model Equationsmentioning

confidence: 99%

“…However, this would not simplify the analysis, and thus, we choose to work with the equations in the form (7) - (9). This follows previous numerical work on this problem [23,2,24,17]. The parameters of interest are the rotation rate Ω and the temperature difference ∆T between the inner and outer annulus walls, because these are the quantities (external variables) that are generally varied in an experiment.…”

Section: Model Equationsmentioning

confidence: 99%

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

Lewis

2010

Physica D: Nonlinear Phenomena

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We present an analysis of the primary bifurcations that occur in a mathematical model that uses the (three-dimensional) Navier-Stokes equations in the Boussinesq approximation to describe the flow of a near unity Prandtl number fluid (i.e. air) in the differentially heated rotating annulus. In particular, we investigate the double Hopf (Hopf-Hopf) bifurcations that occur along the axisymmetric to non-axisymmetric flow transition. Centre manifold reduction and normal forms are used to show that in certain regions in parameter space, stable quasiperiodic mixed-azimuthal mode solutions result as a nonlinear interaction of two bifurcating waves with different azimuthal wave numbers. These flows have been called wave dispersion and interference vacillation. The results differ from similar studies of the annulus with a higher Prandtl number fluid (i.e. water). In particular, we show that a decrease in Prandtl number can equilibrate these mixed-mode solutions.keywords: double Hopf (Hopf-Hopf) bifurcations, quasiperiodic solutions, wave dispersion, axisymmetric to non-axisymmetric transition, rotating waves, centre manifold reduction, numerical approximation of normal form coefficients, Navier-Stokes equations in the Boussinesq approximation PACS: 47.20. Ky, 05.45.a, 47.32.Ef, 47.15.Fe,

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