Stokes Paradox & Theory
Stokes (1851): ∇²ψ² = 0
Stream fn: ψ=U sin(θ)(r − R²/r) [uniform]
Drag: F_D = 6πμRU (Stokes drag, sphere)
Stokes PARADOX (2D cylinder):
No solution at Re=0 in 2D (Whitehead 1889)
Need Oseen correction: Re·(u·∇u) ≠ 0
F_D ≈ 4πμU/[ln(2/Re)−γ] (Oseen-Lamb)
C_D ≈ 24/Re (sphere, Stokes limit)
Reynolds number—
Stokes C_D—
Oseen C_D—
Far-field behavior—