Unsteady Viscous Flows and Stokes's First Problem

Abstract

Unsteady viscous flows and Stokes's first problem are examined. Three problems are considered: unsteady Couette flow, unsteady Poiseuille flow, and unsteady boundary layer flow. The relationship between these three fundamental unsteady flows and Stokes' first problem is illustrated. Scaling principles are used to deduce the short time and long time characteristics of these three problems. Asymptotic analysis is used to obtain exact short and long time characteristics and to show the relationship of each problem to Stokes's first problem for short times. Finally, compact robust models are developed for all values of time using the Churchill-Usagi asymptotic correlation method to combine the short and long time characteristics.