Attached Eddies and Production Spectra in the Atmospheric Logarithmic Layer

Abstract

We investigate the production components of turbulent spectra within logarithmic layers over flat ground. This assumes that the turbulence giving rise to these spectra consists of active coherent structures (eddies) that are attached to the ground, and whose properties display perfect statistical self-similarity under inner scaling. That is, we take the extreme view that active coherent structures not only contribute to turbulence production spectra but explain the whole of them, so that neither detached eddies nor unstructured motions make any significant contribution. Perfect self-similarityis held to apply only to eddies that are themselves formed totally within the log layer, so the theory applies in the limit of spectra obtained at the hearts of very deep log layers. The model predicts that spectral variance and covariance should become independent of wavenumber at small wavenumbers. This asymptotic behaviour is observed in all neutral spectra from the Kansas experiment. The model also interprets the various positions of the spectral peaks observed at Kansas and in aircraft flights over the sea as consequences of the eddies being aggregated into files aligned with the wind. The observed spectra are therefore consistent with large-scale wedge-like structures being the principal component of active turbulence in the neutral atmospheric surface layer.