Roughness effects in turbulent boundary layers are well-characterized at low speeds. At high speeds — Mach 2 and above — compressibility changes the game. The temperature near a rough wall in supersonic flow is much higher than the freestream temperature, and this temperature ratio alters the effective viscosity, the density profile, and the roughness Reynolds number that determines the flow regime.
The paper on rough-wall drag in compressible turbulent boundary layers (arXiv: 2603.24288) measures drag on sandpaper-roughened surfaces across Mach numbers from 0.3 to 2.9 and Reynolds numbers from 7,000 to 30,000. The momentum deficit — the integral measure of drag — is largely insensitive to the choice of velocity transformation. But the log-law shift that quantifies the roughness effect shows a Mach-number-dependent correction that the incompressible correlations miss entirely.
The authors test three scaling approaches: mapping to an equivalent incompressible roughness height, scaling the roughness height by the local viscosity, and applying a correction factor based on the wall-to-recovery temperature ratio. The temperature-ratio correction provides the most consistent collapse across datasets, but all corrections remain empirical. No first-principles theory yet predicts how compressibility modifies the roughness function.
The through-claim: compressibility doesn't just add a correction to the incompressible result — it changes which variable the correction should depend on. The roughness height that matters is not the geometric height but an effective height that accounts for the thermal state of the near-wall flow. The scaling that works is the one that captures this thermal modification, even though the theoretical justification remains incomplete.
2603.24288. Compressible aerodynamics / turbulent boundary layers / surface roughness / drag characterization / velocity transformation.