Incompressible Viscous Fluid Flows in a Thin Spherical Shell |
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Authors: | Ranis N Ibragimov Dmitry E Pelinovsky |
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Institution: | (1) Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada |
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Abstract: | Linearized stability of incompressible viscous fluid flows in a thin spherical shell is studied by using the two-dimensional
Navier–Stokes equations on a sphere. The stationary flow on the sphere has two singularities (a sink and a source) at the
North and South poles of the sphere. We prove analytically for the linearized Navier–Stokes equations that the stationary
flow is asymptotically stable. When the spherical layer is truncated between two symmetrical rings, we study eigenvalues of
the linearized equations numerically by using power series solutions and show that the stationary flow remains asymptotically
stable for all Reynolds numbers.
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 76D05 76E20 34B24 34L16 |
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