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unsteady-laminar-stokes-layerslisted

Use when you must compute the exact unsteady laminar Stokes layer of an infinite plate in a quiescent fluid, either impulsively started or oscillating in its own plane: for the stokes-first-problem Rayleigh layer of a plate started at speed U, evaluate the similarity profile u/U = erfc(y/(2*sqrt(nu*t))), the layer edge at 3.64*sqrt(nu*t) where u/U = 0.01, the wall shear decaying as 1/sqrt(t) from rho*U*sqrt(nu/(pi*t)), and the displacement thickness; for the stokes-second-problem oscillating-plate-layer at omega, evaluate the exponential-cosine velocity field, the penetration depth sqrt(2*nu/omega) with exp(-1) amplitude and 1-rad lag, and the wall shear amplitude rho*U*sqrt(nu*omega) leading the plate velocity by 45 degrees. Produces the closed-form velocity profiles, thicknesses and wall-shear histories in SI units for unsteady shear-layer and viscous time-scale checks. Trigger: unsteady-laminar-stokes-layers, stokes-first-problem, oscillating-plate-layer, rayleigh-layer.
ashfordeOU/aero-agent-skills · ★ 0 · AI & Automation · score 78
Install: claude install-skill ashfordeOU/aero-agent-skills
# Unsteady Laminar Stokes Layers (aerodynamics/boundary-layer/unsteady-laminar-stokes-layers) Use when you must compute the exact unsteady laminar Stokes layer of an infinite flat plate in a quiescent half-space: the closed-form solutions of the one-dimensional vorticity diffusion equation u_t = nu * u_yy for a plate impulsively started at t = 0 (Stokes first problem, the Rayleigh layer) and for a plate oscillating in its own plane (Stokes second problem). The time-dependent layer is the unsteady member of the exact-viscous family whose steady members are already in the tree: the Blasius flat-plate boundary layer (boundary-layer-theory) and the shear-driven Couette gap (compressible-couette-flow). The aeroelasticity leaves cover only inviscid indicial airfoil response, so no existing leaf owns time-dependent laminar shear layers over a plate. Fully closed form, pure stdlib, no iteration. It does not do steady boundary layers, regime classification, Couette gap flow or inviscid oscillating-airfoil aerodynamics; incompressible constant-property laminar flow only, with uniform nu. ## Domain quick reference - Diffusion balance: u_t = nu * u_yy over the half-space y >= 0 above a plate at y = 0 in fluid at rest. Module constants: NU_AIR = 1.46e-5 m2/s, RHO_AIR = 1.225 kg/m3, DELTA99_COEF = 3.6428 (2 * 1.8214, where erfc(1.8214) = 0.01). Dynamic viscosity is always derived mu = rho * nu, never an input. - Stokes first problem (impulsive start, Rayleigh layer): the plate