Boundary layer flow due to the vibration of a sphere. (English) Zbl 1449.76002

Summary: Boundary layer flow of the Newtonian fluid that is caused by the vibration of inner sphere while the outer sphere is at rest is calculated. Vishik-Lyusternik (Nayfeh refers to this method as the method of composite expansions) method is employed to construct an asymptotic expansion of the solution of the Navier-Stokes equations in the limit of high-frequency vibrations for Reynolds number of \(O(1)\). The effect of the Stokes drift of fluid particles is also considered.


76A05 Non-Newtonian fluids
76D05 Navier-Stokes equations for incompressible viscous fluids
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76B99 Incompressible inviscid fluids
Full Text: DOI


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