Low \(Re\) numbers → entire flow is influenced by viscosity → inviscid flow theory not valid

Viscous flow → laminar, smooth orderly flow

↳ Turbulence, irregular, disorderly flow

Transition from laminar to turbulent flow → happens at \(Re = Ud/ν ∼\) 2000 to 3000

\( \nu = \frac{\mu}{\rho}, \quad [\nu] = \frac{m^2}{s} \quad \) (Kinematic viscosity)

z-component of vorticity in 2D flow in x–y plane: \( \frac{D \omega_z}{D t} = \nu \nabla^2 \omega_z \)

↓

\(\nu\) specifies the propensity for vorticity to diffuse through a fluid