Skin Friction in Simple Wall - Bounded Shear Flows in Large Reynolds Number Limit

2009/09/24 by Yakhot, Victor
#FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)

paper · doi:10.48550/arxiv.0909.4387

Abstract

A global approach to analysis of fully developed turbulent flows in pipes/channels and zero pressure gradient boundary layers is proposed. A new dynamic definition of the boundary layer thickness δ(x), where x is the distance to the plate origin, is proposed. The Coles - Fernholtz empirical correlation for skin friction λ=\frac2τ_wρU₀²∝ 1/ln²δ(x) and δ(x)∝ x/ln²(\fracxx₀) are derived from the Navier-Stokes equations in the limit Re_x→ ∞. Here τ_w and U₀ are the wall shear stress and free stream velocity, respectively. The theory is formulated as an expansion in powers of a small dimensionless parameter (dδ(x))/(dx)→ 0 in the limit x→ ∞.

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