A Method for Identifying Kolmogorov’s Inertial Subrange in the Velocity Variance Spectrum

Abstract

AbstractKolmogorov’s inertial subrange is one of the most recognized concepts in fluid turbulence. However, the practical application of this theory to turbulent flows requires identifying subrange bandwidth. In the atmospheric boundary layer, decades of investigation support Kolmogorov’s theory, but the techniques used to identify the subrange vary and no systematic approach has emerged. The algorithm for robust identification of the inertial subrange (ARIIS) has been developed to facilitate empirical studies of the turbulence cascade. ARIIS systematically and robustly identifies the most probable subrange bandwidth in a given velocity variance spectrum. The algorithm is a novel approach in that it directly uses the expected 3/4 ratio between streamwise and transverse velocity components to locate the onset and extent of the inertial subrange within a single energy density spectrum. Furthermore, ARIIS does not assume a −5/3 power law but instead uses a robust, iterative statistical fitting technique to derive the slope over the identified range. This algorithm was tested using a comprehensive micrometeorological dataset obtained from the Floating Instrument Platform (FLIP). The analysis revealed substantial variation in the inertial subrange bandwidth and spectral slope, which may be driven, in part, by mechanical wind–wave interactions. Although demonstrated using marine atmospheric data, ARIIS is a general approach that can be used to study the energy cascade in other turbulent flows.