Viscous Laminar Unsteady Flows - Stokes First Problem

Explore the reformulation of Stokes' first problem through vorticity analysis in this 53-minute lecture. Examine the analogy between vorticity diffusion and momentum diffusion over time, leading to the concept of a mixing layer that evolves from an initial vortex sheet. Analyze the unsteady flow created by an impulsively pulled flat plate bounded by a stationary parallel plate, where the separation distance serves as the characteristic length scale defining the momentum diffusion time scale across the domain. Discover how this solution asymptotically approaches steady-state Couette flow as time approaches the characteristic scale. Draw connections between transient heat conduction in bounded media with fixed temperature plates and momentum diffusion in viscous flow problems, understanding how the parabolic nature of governing equations and analogous boundary conditions create qualitative similarities in temporal evolution of temperature and velocity fields. Conclude with a practical exercise involving the determination of velocity field evolution resulting from impulsive rotation of a cylindrical fluid container.