The friction factor of two-dimensional rough-boundary turbulent soap film flows

Abstract

We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto {\text{Re}}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of ${\text{Re}}^{-1/4}$. For large Re, $f\sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.

4 pages, 3 figures

References in corpus (3)

• Turbulent Friction in Rough Pipes and the Energy Spectrum of the Phenomenological Theory
• Roughness-induced critical phenomena in a turbulent flow
• Intermittency and rough-pipe turbulence

Cited by in corpus (8)

• Turbulence as a problem in non-equilibrium statistical mechanics
• Macroscopic effects of the spectral structure in turbulent flows
• Asymptotic turbulent friction in 2D rough-walled flows
• Drag reduction by polymer additives from turbulent spectra
• Direct Measurement of Turbulent Shear
• The $Re$-number dependence of the longitudinal dispersion in a turbulent channel flow
• Roughness-induced critical phenomenon analogy for turbulent friction factor explained by a co-spectral budget model
• An extension of the momentum transfer model to time-dependent pipe turbulence