Stability of spherical Couette flow in thick layers when the inner sphere revolves

Belyaev, Yu. N.; Monakhov, A. A.; Yavorskaya, I. M.

doi:10.1007/bf01091664

Cited by 23 publications

(20 citation statements)

References 9 publications

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“…7(c) demonstrates that the flow corresponds to the azimuthal wavenumber m = 3. All these observations agree with the experimental and numerical results of [44][45][46]. The period of velocity oscillation T % 18X À1 1 obtained in the present simulations coincides with that in simulations of [46] at slightly supercritical Reynolds number Re 1 = 413.…”

Section: Spherical Coordinatessupporting

confidence: 94%

“…The discrete Laplace operator in bipolar cylindrical coordinates has exactly the same form as in the elliptic cylindrical coordinates (45). The only difference is in h 0 (x 1 , x 2 ) function.…”

Section: Turbulent Flow In Annular Eccentric Pipementioning

confidence: 96%

“…For the numerical test we selected the flow with d = 1.27 and Re 2 = 0, i.e., the large-gap flow with the inner sphere rotation only. It is known from experiments [44,45] and numerical simulations by a spectral method [46] that this flow being steady at low Reynolds number Re 1 becomes unsteady and three-dimensional at supercritical Reynolds numbers. The critical Reynolds number was estimated as Re c = 407 in [44] and Re c = 406 in [46].…”

Section: Spherical Coordinatesmentioning

confidence: 99%

“…The critical Reynolds number was estimated as Re c = 407 in [44] and Re c = 406 in [46]. In [45] was obtained Re c = 406 for a slightly larger gap, d = 1.33. The first unstable mode corresponds to the azimuthal wavenumber m = 3, and the supercritical flows were described in [45,46] as laminar periodic flows with travelling waves in the azimuthal direction, antisymmetric with respect to the equator.…”

Section: Spherical Coordinatesmentioning

confidence: 99%

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Finite-difference method for incompressible Navier–Stokes equations in arbitrary orthogonal curvilinear coordinates

Nikitin

2006

Journal of Computational Physics

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Section: Spherical Coordinatessupporting

confidence: 94%

Section: Turbulent Flow In Annular Eccentric Pipementioning

confidence: 96%

Section: Spherical Coordinatesmentioning

confidence: 99%

Section: Spherical Coordinatesmentioning

confidence: 99%

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Finite-difference method for incompressible Navier–Stokes equations in arbitrary orthogonal curvilinear coordinates

Nikitin

2006

Journal of Computational Physics

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“…counter-rotation, see Liu et al 1996;Loukopoulos & Karahalios 2004). It is unstable with respect to non-axisymmetric perturbations (Belyaev, Monakhov & Yavorskaya 1978;Yavorskaya et al 1986). At high Reynolds numbers (Re ∼ > 10 5 ), the flow develops spiral vortices, shear waves and herringbone waves, before entering a fully developed turbulent state as Re increases further (Nakabayashi & Tsuchida 1988;Nakabayashi et al 2002a, b).…”

Section: Introductionmentioning

confidence: 99%

Superfluid spherical Couette flow

et al. 2008

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We solve numerically for the first time the two-fluid Hall-Vinen-BekarevichKhalatnikov (HVBK) equations for an He-II-like superfluid contained in a differentially rotating spherical shell, generalizing previous simulations of viscous spherical Couette flow (SCF) and superfluid Taylor-Couette flow. The simulations are conducted for Reynolds numbers in the range 1 × 10 2 6 Re 6 3 × 10 4 , rotational shear 0.1 6 Ω/Ω 6 0.3, and dimensionless gap widths 0.2 6 δ 6 0.5. The system tends towards a stationary but unsteady state, where the torque oscillates persistently, with amplitude and period determined by δ and Ω/Ω. In axisymmetric superfluid SCF, the number of meridional circulation cells multiplies as Re increases, and their shapes become more complex, especially in the superfluid component, with multiple secondary cells arising for Re > 10 3 . The torque exerted by the normal component is approximately three times greater in a superfluid with anisotropic Hall-Vinen (HV) mutual friction than in a classical viscous fluid or a superfluid with isotropic Gorter-Mellink (GM) mutual friction. HV mutual friction also tends to 'pinch' meridional circulation cells more than GM mutual friction. The boundary condition on the superfluid component, whether no slip or perfect slip, does not affect the large-scale structure of the flow appreciably, but it does alter the cores of the circulation cells, especially at lower Re. As Re increases, and after initial transients die away, the mutual friction force dominates the vortex tension, and the streamlines of the superfluid and normal fluid components increasingly resemble each other. In non-axisymmetric superfluid SCF, three-dimensional vortex structures are classified according to topological invariants. For misaligned spheres, the flow is focal throughout most of its volume, except for thread-like zones where it is strain-dominated near the equator (inviscid component) and poles (viscous component). A wedge-shaped isosurface of vorticity rotates around the equator at roughly the rotation period. For a freely precessing outer sphere, the flow is equally strain-and vorticity-dominated throughout its volume. Unstable focus/contracting points are slightly more common than stable node/saddle/saddle points in the viscous component, but not in the inviscid component. Isosurfaces of positive and negative vorticity form interlocking poloidal ribbons (viscous component) or toroidal tongues (inviscid component) which attach and detach at roughly the rotation period. 222

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Hydrodynamic stability and bifurcation

Joseph¹

1981

Topics in Applied Physics

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Stability of spherical Couette flow in thick layers when the inner sphere revolves

Cited by 23 publications

References 9 publications

Finite-difference method for incompressible Navier–Stokes equations in arbitrary orthogonal curvilinear coordinates

Finite-difference method for incompressible Navier–Stokes equations in arbitrary orthogonal curvilinear coordinates

Superfluid spherical Couette flow

Hydrodynamic stability and bifurcation

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