An efficient spectral code for incompressible flows in cylindrical geometries

Mercader, Isabel; Batiste, Oriol; Alonso, Arantxa

doi:10.1016/j.compfluid.2009.08.003

Cited by 70 publications

(62 citation statements)

References 49 publications

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“…The spectral solver is based on that described in Ref. [40] and it has been used extensively in a wide variety of enclosed cylinder flows. For the solutions presented here, with = 2, we have used up to n r = 96 and n z = 128 Chebyshev modes in the radial and axial directions.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Rapidly rotating cylinder flow with an oscillating sidewall

Lopez

Marqués

2014

Phys. Rev. E

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We present numerical simulations of a flow in a rapidly rotating cylinder subjected to a time-periodic forcing via axial oscillations of the sidewall. When the axial oscillation frequency is less than twice the rotation frequency, inertial waves in the form of shear layers are present. For very fast rotations, these waves approach the form of the characteristics predicted from the linearized inviscid problem first studied by Lord Kelvin. The driving mechanism for the inertial waves is the oscillating Stokes layer on the sidewall and the corner discontinuities where the sidewall meets the top and bottom end walls. A detailed numerical and theoretical analysis of the internal shear layers is presented. The system is physically realizable, and attractive because of the robustness of the Stokes layer that drives the inertial waves but beyond that does not interfere with them. We show that the system loses stability to complicated three-dimensional flow when the sidewall oscillation displacement amplitude is very large (of the order of the cylinder radius), but this is far removed from the displacement amplitudes of interest, and there is a large range of governing parameters which are physically realizable in experiments in which the inertial waves are robust. This is in contrast to many other physical realizations of inertial waves where the driving mechanisms tend to lead to instabilities and complicate the study of the waves. We have computed the response diagram of the system for a large range of forcing frequencies and compared the results with inviscid eigenmodes and ray tracing techniques.

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Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

Rapidly rotating cylinder flow with an oscillating sidewall

Lopez

Marqués

2014

Phys. Rev. E

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“…19, which can be summarized as follows. To integrate the equations in time, we use the second order time-splitting method proposed in Ref.…”

Section: B Numerical Methodsmentioning

confidence: 99%

Secondary flows in a laterally heated horizontal cylinder

2014

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In this paper we study the problem of thermal convection in a laterally heated, finite, horizontal cylinder. We consider cylinders of moderate aspect ratio (height/diameter approximate to 2) containing a small Prandtl number fluid (sigma < 0.026) typical of molten metals and molten semiconductors. We use the Navier-Stokes and energy equations in the Boussinesq approximation to calculate numerically the basic steady states, analyze their linear stability, and compute some nonlinear secondary flows originated from the instabilities. All the calculated flows and the stability analysis are characterized by their symmetry properties. Due to the confined cylindrical geometry, -presence of lateral walls and lids-, all the flows are completely three dimensional even for the basic steady states. In the range of Prandtl numbers studied, we have identified four different types of instabilities, either oscillatory or stationary. The physical mechanisms, shear or buoyancy, of the corresponding flow transitions have been analyzed. As the value of the Prandtl number approaches sigma = 0.026 the scenario of bifurcations becomes more complicated due to the existence of two different stable basic states originated in a saddle-node bifurcation; a fact that had been overlooked in previous works. (C) 2014 AIP Publishing LLC.Postprint (published version

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“…The details are presented in Mercader et al [35]. We have used n r = 36, n θ = 40 and n z = 64 spectral modes in r, θ and z and a time step dt = 2 × 10 −5 thermal time units in all computations.…”

Section: (B) Pinning In Rotating Rayleigh-bénard Convectionmentioning

confidence: 99%

Bifurcations with imperfect SO(2) symmetry and pinning of rotating waves

et al. 2013

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Rotating waves are periodic solutions in SO(2) equivariant dynamical systems. Their precession frequency changes with parameters and it may change sign, passing through zero. When this happens, the dynamical system is very sensitive to imperfections that break the SO(2) symmetry and the waves may become trapped by the imperfections, resulting in steady solutions that exist in a finite region in parameter space. This is the so-called pinning phenomenon. In this study, we analyse the breaking of the SO(2) symmetry in a dynamical system close to a Hopf bifurcation whose frequency changes sign along a curve in parameter space. The problem is very complex, as it involves the complete unfolding of high codimension. A detailed analysis of different types of imperfections indicates that a pinning region surrounded by infinite-period bifurcation curves appears in all cases. Complex bifurcational processes, strongly dependent on the specifics of the symmetry breaking, appear very close to the intersection of the Hopf bifurcation and the pinning region. Scaling laws of the pinning region width and partial breaking of SO(2) to Z m are also considered. Previous as well as new experimental and numerical studies of pinned rotating waves are reviewed in the light of the new theoretical results.

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An efficient spectral code for incompressible flows in cylindrical geometries

Cited by 70 publications

References 49 publications

Rapidly rotating cylinder flow with an oscillating sidewall

Rapidly rotating cylinder flow with an oscillating sidewall

Secondary flows in a laterally heated horizontal cylinder

Bifurcations with imperfect SO(2) symmetry and pinning of rotating waves

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