The partitioning of attached and detached eddy motion in the atmospheric surface layer using Lorentz wavelet filtering

Abstract

Townsend's attached eddy hypothesis states that the turbulent structure in the constant stress layer can be decomposed into attached and detached eddy motion. This paper proposes and tests a methodology for separating the attached and detached eddy motion from time series measurements of velocity and temperature. The proposed methodology is based on the time-frequency localization and filtering capabilities of the orthonormal wavelet transforms. Using a relative entropy statistical measure, the optimal wavelet basis is identified first. The turbulence time series measurements are then transformed into the wavelet domain where the contribution of specific events in the time-frequency domain is identified. The filtering scheme utilizes a recently constructed Lorentz thresholding methodology that successfully eliminates all wavelet coefficients associated with the detached eddy motion. While this filtering scheme lacks the compression efficiency of the classical Donoho and Johnstone's universal thresholding model, it conserves the higher-order statistics and important turbulence interactions related to the Reynolds stresses. Following the filtering scheme, the attached eddy motion time series is re-constructed by an inverse wavelet transform of the non-zero wavelet coefficients. The proposed partitioning methodology for attached and detached eddy motion is tested using 56 Hz triaxial sonic anemometer velocity and temperature measurements above a uniform dry lake bed in Owens valley, California, for a wide range of atmospheric stability conditions. Validation that the wavelet filtered time series represents the attached eddy motion is also discussed in the context of conservation of turbulence energy and surface fluxes.