THE PARTITIONING OF ATTACHED AND DETACHED EDDY MOTION IN THE ATMOSPHERIC SURFACE-LAYER USING LORENTZ WAVELET FILTERING

Townsend's attached eddy hypothesis states that the turbulent structur e in the constant stress layer can be decomposed into attached and det ached eddy motion. This paper proposes and tests a methodology for sep arating the attached and detached eddy motion from time series measure ments of velocity and temperature. The proposed methodology is based o n the time-frequency localization and filtering capabilities of the or thonormal wavelet transforms. Using a relative entropy statistical mea sure, the optimal wavelet basis is identified first. The turbulence ti me series measurements are then transformed into the wavelet domain wh ere the contribution of specific events in the time-frequency domain i s identified. The filtering scheme utilizes a recently constructed Lor entz thresholding methodology that successfully eliminates all wavelet coefficients associated with the detached eddy motion. While this fil tering 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 o f the non-zero wavelet coefficients. The proposed partitioning methodo logy for attached and detached eddy motion is tested using 56 Hz triax ial sonic anemometer velocity and temperature measurements above a uni form dry lake bed in Owens valley, California, for a wide range of atm ospheric stability conditions. Validation that the wavelet filtered ti me series represents the attached eddy motion is also discussed in the context of conservation of turbulence energy and surface fluxes.