Revisiting Stokes' first problem for Maxwell fluids

Abstract

Stokes' first problem for Maxwell fluids is re-examined and new findings are presented. Specifically, the behaviour of the velocity field is examined with respect to vortex sheet and jump amplitude structure, expressions for the boundary layer thickness are given, and an energy analysis is carried out. Several new small-time expressions are derived for both velocity- and energy-related quantities. Results for Maxwell fluids are compared with those of viscous Newtonian fluids and analytical findings are supported by numerical work. It is shown that the presence of fluid elasticity counteracts viscous effects, that the Maxwell and viscous Newtonian kinetic energy profiles intersect, and that the point of intersection is both greater than and proportional to the Maxwell relaxation time. © Oxford University Press 2005; all rights reserved.