The influence of coherent structures and microfronts on scaling laws using global and local transforms

Abstract

This study examines the influence of coherent structures and attendant microfronts on scaling laws. Toward this goal, we analyse atmospheric observations of turbulence collected 45 m above a flat surface during the Lammefjord Experiment in Denmark. These observations represent more than 40 hours of nearly stationary strong wind conditions and include more than 1600 samples of the main coherent structures. These samples occupy about 40% of the total record and explain the majority of the Reynolds stress.To study the dependence of the scaling laws on the choice of basis set, the time series of velocity fluctuations are decomposed into Fourier modes, the local Haar basis set and eigenvectors of the lagged covariance matrix. The three decompositions are compared by formulating joint projections. The decompositions are first applied to the samples of phased-locked coherent structures centred about eddy microfronts. The eigenvector decomposition is able to partially separate the small-scale variances due to the coherent eddy microfronts from that due to the small-scale structure with random phase. In the Fourier spectrum, both of these contributions to the variance appear together at the higher wavenumbers and their individual contributions cannot be separated. This effect is relatively minor for the scale distribution of energy but exerts an important influence on higher-moment statistics. Deviations from the −$\frac53$ scaling are observed to be slight and depend on choice of basis set.The microfronts strongly influence the higher-order statistics such as the sixth-order structure function traditionally used to estimate the energy transfer variance. The intermittency of fine-scale structure, energy transfer variance and dissipation are not completely characterized by random phase, as often assumed, but are partly associated with microfronts characterized by systematic phase with respect to the main transporting eddies. These conclusions are supported by both the higher-order structure function and the higher-order Haar transform.The Fourier and Haar spectra are also computed for the entire record. The peak of the Haar energy spectrum occurs at smaller scales than those of the Fourier spectrum. The Haar transform is local and emphasizes the width of the events. The Fourier spectrum peaks at the scale of the main periodicity, if it exists, which includes the spacing between the events.