Multiscale interactions between surface shear stress and velocity in turbulent boundary layers

Understanding and quantifying the multiscale interactions between surface shear stress and velocity in the boundary layer is essential to improving boundary condition parameterizations used in numerical models of turbulent boundary layers. In this study, high-frequency measurements obtained in a wind tunnel are used to identify dominant scales of interaction (quantified in terms of scale-dependent linear correlation) between wind velocity and shear stress via wavelet cross-correlation analysis. Three ranges of scales of interaction are identified: (1) in the inertial subrange the correlation is negligible; (2) in the energy production range the correlation follows a logarithmic law and exhibits scale invariance under normalization of scale with distance to the surface, z; and (3) for scales larger than the boundary layer height, δ, the correlation reaches a plateau value which is a function of z/δ. Our results allow us to estimate the linear correlation between shear stress and wind velocity at multiple scales and assess the reliability of typical boundary condition formulations in numerical models (for instance, large-eddy simulation) that compute shear stress (or its fluctuations) as a linear function of wind velocity at the first vertical grid point.