Some Thoughts On Local Isotropy And The 4/3 Lateral To Longitudinal Velocity Spectrum Ratio

Applications of Kolmogorov's universal equilibrium hypothesis and the Taylor transform to velocity spectra derived from measurements within the low frequency portion of the atmospheric surface layer (ASL) inertial subrange are examined. The measured ratios of lateral to longitudinal velocity component spectra exhibit considerable scatter, but suggest convergence towards 1.0 rather than towards the 4/3 expected from theory. Shear and buoyancy introduce anisotropy to the inertial subrange, thereby contributing to the observed scatter. The apparent discrepancy between the 4/3 velocity component spectrum ratio expected from theory and the measurements could arise as a consequence of the processing used to produce spectra. These processing effects must be considered from the perspective of the propagating eddy. Spectral averaging used with sonic anemometer data is done over time periods that are large with respect to inertial subrange eddy correlation decay times. This averaging causes energy from larger scale eddies to appear as `local convection' that dominates the Taylor transform. Spectrum ratio convergence and cospectra approaching zero are necessary, but not sufficient, conditions for onset of local isotropy. Measurements of spectrum ratios and cospectra over the entire inertial subrange are needed to determine whether or not local isotropy might occur within the ASL.