Perturbed Roughness Sublayer affecting the law of thewall modeled by a "co-spectral link"

 

Fully developed turbulent flows near walls, regardless of their roughness, are commonly studied based on the law of the wall originally proposed by Prandtl and von Karman in the early part of the 20th century. The derivation of the law of the wall has traditionally been based on theoretical and scaling arguments, under which a balance between dissipation and production (negligible advection terms) of turbulent kinetic energy and a nearly constant shear stress with distance from the wall are assumed in a thin layer of fluid, accommodating about 10% of the boundary layer (i.e., separation of scales). One of the hallmarks of this theory is the von-Karman constant (=0.4) valid across many wall-roughness and boundary layer flow configurations. In many situations, however, the separation of scales required to observe a log-layer is hardly realizable, especially in tall and fully rough canopy flows as in submerged aquatic vegetation and urban centres under certain atmospheric conditions. In recent years, several spectral- and co-spectral -based theories have revealed a "link" between the law of the wall and the energy spectrum of turbulent eddies. This link is exploited here to examine the roughness sublayer of a rough canopy boundary layer. A simplified co- spectral model and data collected from wind tunnel experiments allows to examine the roughness sublayer correction to the law of the wall and test the effect of finite Reynolds number and intermittency on the von-Karman constant, from which the scales dominating the law of the wall in the roughness sublayer are revealed.