THE INFLUENCE OF COHERENT STRUCTURES AND MICROFRONTS ON SCALING LAWS USING GLOBAL AND LOCAL TRANSFORMS

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 mo re than 40 hours of nearly stationary strong wind conditions and inclu de more than 1600 samples of the main coherent structures. These sampl es occupy about 40% of the total record and explain the majority of th e Reynolds stress. To study the dependence of the scaling laws on the choice of basis set, the time series of velocity fluctuations are deco mposed into Fourier modes, the local Haar basis set and eigenvectors o f 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 edd y microfronts. The eigenvector decomposition is able to partially sepa rate the small-scale variances due to the coherent eddy microfronts fr om that due to the small-scale structure with random phase. In the Fou rier spectrum, both of these contributions to the variance appear toge ther at the higher wavenumbers and their individual contributions cann ot be separated. This effect is relatively minor for the scale distrib ution of energy but exerts an important influence on higher-moment sta tistics. Deviations from the -5/5 scaling are observed to be slight an d depend on choice of basis set. The microfronts strongly influence th e higher-order statistics such as the sixth-order structure function t raditionally used to estimate the energy transfer variance. The interm ittency of fine-scale structure, energy transfer variance and dissipat ion are not completely characterized by random phase, as often assumed , but are partly associated with microfronts characterized by systemat ic phase with respect to the main transporting eddies. These conclusio ns are supported by both the higher-order structure function and the h igher-order Haar transform. The Fourier and Haar spectra are also comp uted for the entire record. The peak of the Haar energy spectrum occur s at smaller scales than those of the Fourier spectrum. The Haar trans form is local and emphasizes the width of the events. The Fourier spec trum peaks at the scale of the main periodicity, if it exists, which i ncludes the spacing between the events.