The spatial structure of neutral atmospheric surface-layer turbulence

TLDR

Neutral atmospheric boundary‑layer turbulence is often modeled assuming a linear velocity profile across the height interval of interest. The study attempts to model the complete second‑order structure of homogeneous, neutrally stratified atmospheric boundary‑layer turbulence, including all velocity component spectra and cross‑spectra between any two points. Two Rapid Distortion Theory–based models, differing only in whether surface blocking is included, are constructed using the linearized Navier–Stokes equations and eddy‑lifetime considerations, with three adjustable parameters (largest eddy lengthscale, eddy‑lifetime number, and energy‑dissipation measure), and calibrated against two year‑long atmospheric experiments. Despite their crude assumptions, the models accurately predict two‑point second‑order statistics such as cross‑spectra, coherences, and phases from single‑point measurements, with only minor differences in vertical‑velocity coherences attributable to surface blocking.

Abstract

Modelling of the complete second-order structure of homogeneous, neutrally stratified atmospheric boundary-layer turbulence, including spectra of all velocity components and cross-spectra of any combination of velocity components at two arbitrarily chosen points, is attempted. Two models based on Rapid Distortion Theory (RDT) are investigated. Both models assume the velocity profile in the height interval of interest to be approximately linear. The linearized Navier–Stokes equation together with considerations of ‘eddy’ lifetimes are then used to modify the spatial second-order structure of the turbulence. The second model differs from the first by modelling the blocking by the surface in addition to the shear. The resulting models of the spectral velocity tensor contain only three adjustable parameters: a lengthscale describing the size of the largest energy-containing eddies, a non-dimensional number used in the parametrization of ‘eddy’ lifetime, and the third parameter is a measure of the energy dissipation. Two atmospheric experiments, both designed to investigate the spatial structure of turbulence and both running for approximately one year, are used to test and calibrate the models. Even though the approximations leading to the models are very crude they are capable of predicting well the two-point second-order statistics such as cross-spectra, coherences and phases, on the basis of measurements carried out at one point. The two models give very similar predictions, the largest difference being in the coherences involving vertical velocity fluctuations, where the blocking by the surface seems to have a significant effect.