Drag of a sphere in an unsteady flow of viscous fluid at small Reynolds numbers (Q1115700)

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 \((R_ k)\) 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 \(R\to 0\), \(R_ k\to 0\).