From Spectral–Covariance Transfer to Validated Engineering Wall Laws: Nikuradse Roughness, Closure Discrimination, and Riblet Transport Diagnostics

This paper develops a traceable engineering reduction from a spectral–covariance reconstruction of forced incompressibleNavier–Stokes dynamics and then subjects the resulting walllaw architecture to two complementary external tests. Themathematical reduction retains the source carrier normalization, pulse-age normalization, energy-metric correction, exact frozenprojection to physical wall coordinates, and the exact pipe meanmomentum balance before any friction approximation.