Justification of the Inertial Dissipation Technique in Anisotropic Mean Flow

Abstract

The inertial dissipation technique has been successfully employed for many years to measure the wind stress, especially over the open ocean. This method is based on Kolmogorov's theoretical prediction of universality in the inertial wavenumber range. The theory was developed under the assumption of locally isotropic turbulence, and the dissipation technique has been criticized as lacking justification in a boundary-layer shear flow. In this paper, Kolmogorov's theory is explicitly applied to the anisotropic conditions prevailing in the atmosphere. It is shown that the inertial dissipation method relies on the homogeneity and isotropy of the spectrum φii(k) for k in the inertial range. This is a weaker condition than Kolmogorov's assumption of isotropy of the correlation function Bij(r). In high-Reynolds-number shear flows, isotropy of φii(k) is realized to a good approximation, whereas isotropy of Bij(r) is not. Some consequences for the experimental implementation are discussed; in particular, sampling times (block lengths) not exceeding the order of the eddy life time are recommended in the calculation of spectra.