Research Theme

Turbulence and the Wall

We develop first-principles theories of wall friction that connect roughness, Reynolds number, and energy dissipation through turbulence spectra— unifying classical empirical diagrams into mechanistic scaling laws.

Wall Friction Roughness & Reynolds Turbulence Spectra

Why wall friction is a fundamental turbulence problem

A central challenge in fluid mechanics is explaining energy dissipation in turbulent flows arising from friction at boundaries. This “wall friction” problem directly controls pressure drop and transport efficiency in pipelines and channels—critical for moving oil, methane, and water across continents.

Classical practice relies on empirical Nikuradse/Moody diagrams linking friction factor to Reynolds number and relative roughness. Our goal is to replace curve-fitting with a first-principles mechanism grounded in turbulence theory.

A mechanistic framework: spectra, budgets, and universality

📉 Co-spectral budget closure

Use a turbulence co-spectral budget model to connect wall roughness to dissipation across scales, yielding friction-factor predictions from underlying physics.

🧭 Unified friction-factor curve

Derive a single unifying formulation that bridges laminar and turbulent regimes and collapses classical diagrams into one mechanistic curve.

🧩 Critical-point analogy

Interpret roughness-induced transitions through a critical phenomenon lens, clarifying when and why friction-factor scaling changes across regimes.

What this framework enables

First-principles prediction of friction factor from turbulence spectra
A unified view of Nikuradse/Moody behavior across regimes
Mechanistic interpretation of roughness transitions and critical points
Improved transport modeling for pipelines, channels, and engineered networks

Representative Publications

Li, S., & Katul, G. (2021). Roughness-induced critical phenomenon analogy for turbulent friction factor explained by a co-spectral budget model. Physics of Fluids, 33(10).
Wang, W. J., Li, S., Huang, W., Han, Z., & Wang, W. H. A unified friction factor formulation: Bridging laminar and turbulent friction factor with critical points analysis. Physics of Fluids, 36(1).