In turbulent boundary layer modeling, roughness shifts the logarithmic velocity profile downward — the flow behaves as if the wall were somewhere else. The standard approach specifies an equivalent sand-grain roughness height, but mapping real surface roughness to this parameter requires empirical correlations that may not transfer between flow configurations.
The paper on modifying the k-omega-zero model for roughness (arXiv: 2603.22737) takes a different route. The k-omega-zero model already uses a transformation that moves the wall-normal coordinate origin; the extension adds an effective origin shift for rough surfaces. The log-layer offset is then computed as a function of this effective origin, creating a direct correspondence between the geometric parameter (effective origin) and the aerodynamic parameter (equivalent sand-grain roughness).
The authors derive a formula for the virtual origin of the fully rough log law and show that the model recovers the correct fully rough limit — the regime where viscous effects at the wall become negligible and the roughness alone determines the friction.
The through-claim: roughness in turbulence modeling is a coordinate problem before it's a physics problem. The flow over a rough wall is the flow over a smooth wall displaced to a different origin, with corrections. Getting the displacement right — the virtual origin — matters more than elaborating the turbulence model itself. The simplest modification that captures the correct asymptotic behavior (the fully rough limit) constrains the model more powerfully than a complex modification that doesn't.
2603.22737. Turbulence modeling / surface roughness / k-omega model / boundary layer / virtual origin.