Turbulent Boundary Layer — Log-Law of the Wall
von Kármán log profile, viscous sublayer, buffer layer, and outer region
Parameters
Friction velocity u_τ:
1.00
Kinematic viscosity ν (×10⁻³):
1.50
von Kármán constant κ:
0.41
Additive constant B:
5.00
Wall roughness ks⁺:
0.0
Display mode:
Log axis (y⁺)
Linear y
δ_ν (viscous length) =
—
Re_τ (friction Re) =
—
u_τ⁺ at y⁺=1:
—
Viscous sublayer (y⁺ < 5):
u⁺ = y⁺
Log layer (y⁺ > 30):
u⁺ = (1/κ)ln(y⁺) + B
Rough wall:
B → B−ΔB(ks⁺)
y⁺ = y·u_τ/ν u⁺ = u/u_τ
κ ≈ 0.41 (von Kármán 1930) is universal across flows. The log law spans 3 decades in high-Re flows.