Unsteady viscous ! ows and Stokes's " rst problem

Unsteady viscous ! ows and Stokes's " rst problem are examined. Three problems are considered: unsteady Couette ! ow, unsteady Poiseuille ! ow, and unsteady boundary layer ! ow. The relationship between these three fundamental unsteady ! ows and Stokes' " rst 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 " rst problem for short times. Finally, compact robust models are developed for all values of time using the ChurchilleUsagi asymptotic correlation method to combine the short and long time characteristics.