Rayleigh problem

The Rayleigh problem describes unsteady viscous flow generated when an infinite flat plate is impulsively set in motion parallel to itself through stationary fluid.

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Diffusion equation: A partial differential equation describing how a quantity spreads through a medium over time. The plate’s velocity field obeys this equation as momentum diffuses into the fluid.
Navier–Stokes equations: Nonlinear partial differential equations governing the motion of viscous fluids. The Rayleigh problem is a special solution of these governing equations.
Stokes' second problem: The oscillatory viscous flow produced by an infinite plate moving periodically parallel to itself. It replaces the sudden start with periodic motion to test related unsteady-flow predictions.
Couette flow: Viscous flow between surfaces driven by their relative motion. Steady Couette flow is bounded by surfaces, unlike the transient flow beside one infinite plate.
Kinematic viscosity: The ratio of a fluid’s dynamic viscosity to its density, measuring momentum diffusivity. It sets the rate at which the plate’s motion spreads into the fluid.
No-slip condition: A boundary condition stating that fluid at a solid surface has the surface’s velocity. It makes the fluid next to the plate move with the plate immediately.
Wall shear stress: The tangential stress exerted by a fluid on a boundary. The solution predicts how the plate’s resisting shear changes after startup.
Lamb–Oseen vortex: An exact viscous solution describing the diffusion of vorticity from a concentrated line vortex. It also demonstrates viscous diffusion, but spreads rotational motion radially rather than from a wall.
Error function: A special function arising in solutions of diffusion equations and probability theory. The exact velocity profile is expressed using this function.
Unsteady flow: Fluid motion whose velocity or other properties vary with time at a fixed location. The fluid accelerates over time after the plate starts moving.