Flow Parameters
Theory
y⁺ = y·u_τ/ν, u⁺ = u/u_τ
Viscous sublayer (y⁺<5): u⁺ = y⁺
Log layer (y⁺>30): u⁺ = (1/κ)ln(y⁺)+B
Buffer layer (5<y⁺<30)
Rough: ΔU⁺ = (1/κ)ln(1+k⁺)
Turbulent
Laminar
Log law
u⁺=y⁺
Derived Quantities
U_bulk⁺—
δ_viscous—
δ_log start—
c_f×10³—
ΔU⁺(rough)—
κ≈0.41 (von Kármán) and B≈5.2 are universal constants. Turbulent profiles carry far more momentum flux — much flatter than parabolic laminar. Re_τ = u_τ·δ/ν (friction Reynolds number).