Analytical model for the streamwise-velocity linear coherence spectrum inspired from Townsend's attached eddy hypothesis: Assessment against wind LiDAR measurements of the near-neutral atmospheric surface layer*

The inertial layer of high Reynolds-number wall-bounded flows is populated by eddies of different typologies inducing streamwise velocity fluctuations characterized by wavelengths either constrained by the boundary layer height (Δ_E), or much larger than Δ_E, which are denoted as Very-Large-Scale Motions (VLSMs). For the former, and specifically for velocity fluctuations associated with wall-attached eddies, Townsend provided a theoretical framework to predict their organization and turbulence statistics. Inspired by that theory, an analytical model is proposed for the Linear Coherence Spectrum (LCS) of the streamwise velocity to identify the spectral footprint and turbulence intensity associated with wall-attached eddies and VLSMs. The proposed LCS model is based on three parameters: the eddy aspect ratio (AR), the isolated-eddy contribution to the LCS (C₁), and an offset parameter (C₃) introduced to account for the presence of VLSMs. The model is assessed against streamwise velocity measurements performed with a scanning pulsed Doppler LiDAR in the near-neutral atmospheric surface layer (ASL). The results show that the maximum height attained by wall-coherent structures is equal to 0.31Δ_E and the low-wavelength boundary of the VLSMs spectral region corresponds to roughly 4.5Δ_E.