Abstract
An unsteady flow of viscous incompressible fluid past a sphere is investigated. The values of the inertial and unsteady terms in the Navier-Stokes equations are characterized by translational (R) and vibrational (Rk) Reynolds numbers, which are assumed small. The solution is constructed in the form of an expansion with respect to max(R, R k 1/2 ) by the method of matched asymptotic expansions. A correction to the Stokes force, correct to o[max(R, R k 1/2 )], is calculated. It is shown that the result depends strongly on the ratio R/R k 1/2 and goes over into the well-known equations for the cases R → 0, Rk→ 0.
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