The unsteady stokeslet and oseenlet

Abstract

The unsteady low Reynolds number flow of an incompressible viscous fluid past a singular forcelet is investigated analytically. New fundamental three-dimensional solutions for a concentrated impulsive force are derived for the Stokes and the Oseen equations. These elementary solutions can be used as fundamental Green's functions to obtain solutions for flows over singularities with any time-dependent nature. The fundamental singularities are employed to construct some well-known solutions to demonstrate their validity and usefulness in solving unsteady problems governed by the Stokes and the Oseen equations. A new solution is presented for an unsteady Oseen flow with a constant acceleration.