Turbulent Boundary Layer — Law of the Wall

Inner/outer scaling, viscous sublayer, log layer, wake region

U⁺ vs y⁺ (wall units, semi-log)

Flow visualization

Eddy viscosity ν_t(y)

Reynolds stress -⟨u'v'⟩

Turbulent kinetic energy k

Reynolds τ_w (shear stress, Pa) 0.100 Kinematic viscosity ν (m²/s ×10⁻⁶) 1.0 BL thickness δ (mm) 10 von Kármán κ 0.410 Log-law constant B 5.1

Law of the wall: U⁺=y⁺ (viscous sublayer, y⁺<5), U⁺=(1/κ)·ln(y⁺)+B (log layer, 30<y⁺<200), wake function for outer region. Wall units: u_τ=√(τ_w/ρ), y⁺=yu_τ/ν, U⁺=U/u_τ.
Friction velocity u_τ: — m/s | Viscous length: — μm | δ⁺ = — | Re_τ = —