Turbulent Boundary Layer — Log Law of the Wall
von Kármán Constant κ ≈ 0.41 | Viscous Sublayer | Buffer Layer | Log Region
Boundary Layer Parameters
von Kármán constant κ:
0.410
Additive constant B:
5.20
Reynolds number Re_θ:
5000
Pressure gradient dP/dx:
0.00
Kinematic viscosity ν (×10⁻⁶):
1.50
Viscous sublayer
(y⁺ < 5): u⁺ = y⁺ (linear, viscous shear dominates).
Buffer layer
(5 < y⁺ < 30): transition region, Spalding law interpolates.
Log region
(y⁺ > 30): u⁺ = (1/κ)·ln(y⁺) + B, where u⁺ = u/u_τ, y⁺ = y·u_τ/ν, u_τ = √(τ_w/ρ).
Wake region
: outer layer correction (Coles wake parameter). Skin friction: C_f = τ_w/(½ρU²). Clauser chart uses log law to infer u_τ from velocity profiles experimentally. κ=0.41, B=5.2 are empirical constants confirmed across many flows.