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Transitional vortices in wide-gap spherical annulus flow. (English) Zbl 1092.76027
Summary: We develop a semianalytic formulation suitable for solving Navier-Stokes equations governing the induced steady axially symmetric motion of incompressible viscous fluid confined in a wide gap between two differentially rotating concentric spheres. The method is valid for arbitrarily high Reynolds number and aids in the presentation of multiple steady-state flow patterns and their bifurcations. In the case of a rotating inner sphere and a stationary outer sphere, linear stability analysis is conducted to determine whether or not the computed solutions are stable. It is found that the solution transforms smoothly into an unstable solution beginning with asymmetric vortex pairs identified near the point of a symmetry-breaking bifurcation which occurs at Reynolds number 589. This solution transforms smoothly into an unstable asymmetric vortex solution as the Reynolds number increases. Flow modes whose branches have not been previously reported are found using this method. The origin of the flow modes is discussed using bifurcation theory.

MSC:
76E07 Rotation in hydrodynamic stability
76U05 General theory of rotating fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76D17 Viscous vortex flows
Software:
MATCONT
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