Stability of Couette flow between two rotating cylinders

Shapakidze, L. D.

doi:10.1007/bf01015277

Cited by 3 publications

(5 citation statements)

References 4 publications

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“…Problem (1.1), (1.2) admits an exact solution [6,7] which is the basic steady rotationally symmetric flow with nonzero radial and azimuthal components of the velocity vector:…”

Section: Constitutive Equations and Basic Regimementioning

confidence: 99%

Occurrence of quasiperiodic flows between two rotating permeable cylinders

Колесов

Romanov

2014

J Appl Mech Tech Phy

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This paper considers viscous incompressible fluid flows between two infinite rotating permeable concentric cylinders near the bifurcation point, which result in secondary steady flow and oscillations with azimuthal waves. Steady periodic and quasiperiodic fluid flow regimes with two, three, and four independent frequencies are obtained by methods of the theory of codimension-two bifurcations of hydrodynamic flows having cylindrical symmetry.

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“…Problem (1.1), (1.2) admits an exact solution [6,7] which is the basic steady rotationally symmetric flow with nonzero radial and azimuthal components of the velocity vector:…”

Section: Constitutive Equations and Basic Regimementioning

confidence: 99%

Occurrence of quasiperiodic flows between two rotating permeable cylinders

Колесов

Romanov

2014

J Appl Mech Tech Phy

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“…The calculations made in [6][7][8] showed that with increase in the Reynolds number flow (1.4) can lose stability in two ways. As a result of monotonic rotational-symmetric instability a secondary stationary flow pattern arises (the calculations using direct numerical integration of problem (2.2) were carried out in [11]).…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…The further increase in the Reynolds number leads to complication of the fluid flow structure and gives rise to different complicated regimes and then to turbulence.The calculations of neutral curves made it possible to found that at certain parameter values the curves corresponding to rotational-symmetric and oscillatory three-dimensional instabilities intersect [4][5][6][7][8].In the mid-eighties of the last century V.I. Yudovich in Russia and J. Iooss and P. Chossat in France devised the bifurcation theory of codimension two for hydrodynamic flows with cylindrical symmetries.…”

mentioning

confidence: 99%

“…The calculations of neutral curves made it possible to found that at certain parameter values the curves corresponding to rotational-symmetric and oscillatory three-dimensional instabilities intersect [4][5][6][7][8].…”

mentioning

confidence: 99%

“…for any real δ and h. Problem (1.1), (1.2) admits an exact solution [4,5] which represents the main stationary rotationalsymmetric flow with nonzero radial component of the velocity vector…”

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confidence: 99%

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Chaos generation in the Couette-Taylor problem for permeable cylinders

Колесов¹,

Romanov²

2013

Fluid Dyn

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The methods of the bifurcation theory of codimension two, together with computer calculations, are used to investigate stationary, periodic, and quasiperiodic flows with two and three independent frequencies, as well as chaotic regimes of fluid flow between two infinite rotating permeable concentric cylinders near the intersection of the bifurcations initiating secondary stationary flow and self-oscillations with azimuthal waves.The experimental investigations [1][2][3] have shown that with increase in the Reynolds number the main stationary rotational-symmetric fluid flow between two rotating permeable cylinders changes for a secondary stationary flow or a self-oscillatory regime with waves traveling in the azimuthal direction. The further increase in the Reynolds number leads to complication of the fluid flow structure and gives rise to different complicated regimes and then to turbulence.The calculations of neutral curves made it possible to found that at certain parameter values the curves corresponding to rotational-symmetric and oscillatory three-dimensional instabilities intersect [4][5][6][7][8].In the mid-eighties of the last century V.I. Yudovich in Russia and J. Iooss and P. Chossat in France devised the bifurcation theory of codimension two for hydrodynamic flows with cylindrical symmetries. This made it possible to investigate different fluid flow regimes in the vicinity of the point of intersection of bifurcations of the origin of secondary stationary flow and azimuthal waves for impermeable cylinders [9,10]. In this study, this theory is applied for calculating complicated fluid flows in the Couette-Taylor problem for permeable cylinders. GOVERNING EQUATIONS AND MAIN REGIMELet a gap between two solid infinite permeable concentric cylinders, R 1 and R 2 in radii (R 1 < R 2 ) rotating at angular velocities Ω 1 and Ω 2 be filled with a viscous homogeneous incompressible fluid. We will assume that there are no external body forces. The quantities R 1 , Ω 1 R 1 ,a nd 1/Ω 1 are taken for the length, velocity, and time scales, respectively.In the cylindrical coordinates r, ϕ, z, with the z axis aligned with the cylinder axis, the dimensionless Navier-Stokes and continuity equations take the form:

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On the pointwise stability of a viscous liquid between rotating coaxial cylinders

Rosso¹

1984

Journal of Mathematical Analysis and Applications

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Stability of Couette flow between two rotating cylinders

Cited by 3 publications

References 4 publications

Occurrence of quasiperiodic flows between two rotating permeable cylinders

Occurrence of quasiperiodic flows between two rotating permeable cylinders

Chaos generation in the Couette-Taylor problem for permeable cylinders

On the pointwise stability of a viscous liquid between rotating coaxial cylinders

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