Couette & Shear Flow
Viscous fluid between moving plates: laminar vs turbulent regimes
Couette flow: viscous fluid between two plates, top plate moving at velocity U. Laminar solution: u(y) = U·y/h (linear profile). Reynolds number Re = ρUh/μ. At Re ≫ 1, the flow becomes turbulent, developing a nearly flat core with thin boundary layers. Shear stress τ = μ·du/dy = μU/h. This models lubrication in bearings, blood flow in vessels, and the mantle flow driving tectonic plates.