Linearized velocity disturbances and dynamic Oseen tensors in simple shear and elongational flows

Abstract

We investigate the velocity disturbance produced by point-like sources of force in viscous fluids subjected to unbounded, simple shear, and elongational flows of arbitrary strength. The response to the body force is given by the dynamic Oseen tensor which is constructed using the propagator for the linearized Navier–Stokes equation. Application of the method of characteristics leads to ‘‘Kelvin mode’’-type solutions for the velocity disturbances and explicit analytical expressions are obtained for the propagators and Oseen tensors in the above mentioned flows.