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

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 $\delta (x)$, where $x$ is the distance to the plate origin, is proposed. The Coles - Fernholtz empirical correlation for skin friction $\lambda =\frac{2{\tau }_w}{\rho U_0^2}\propto 1/{\ln }^2\delta (x)$ and $\delta (x)\propto x/{\ln }^2(\frac{x}{x_0})$ are derived from the Navier-Stokes equations in the limit $R{e}_x\to \infty$. Here ${\tau }_w$ and $U_0$ are the wall shear stress and free stream velocity, respectively. The theory is formulated as an expansion in powers of a small dimensionless parameter $\frac{d\delta (x)}{dx}\to 0$ in the limit $x\to \infty$.

substantially reworked and corrected version

References in corpus (2)

• Probability Densities in Strong Turbulence
• Statistics of velocity gradients in wall-bounded shear flow turbulence