A physically-based turbulent velocity time series decomposition

Single-point, three-component turbulent velocity time series data obtained in the atmospheric boundary layer over the ocean reveal coherent structures that are consistent with a model of a steady linearly varying spatial velocity field that translates past the measurement point at constant velocity. The kinematic model includes both strain and rotation rates and has implications regarding vortex generation, vortex pairing, vortex break-up, and stability. While the complete specification of the dimensions, spatial velocity gradients, and translational velocity of the linear coherent structure (LCS) cannot be made from the single-point, three-component measurements, the model LCS velocity time series can be determined from least-squares fits to the data. The total turbulent kinetic energy is used to find in the record the initial and final times of a model LCS in the data, i.e., the time interval over which a model LCS is passing over the anemometer. Maxima in the kinetic energy removed from the data (by subtraction of the model LCS velocity functions from the data) are used to identify the most-energetic model LCSs. These model LCS velocity functions replicate the essential large-scale features of the time series of the three-component velocity fluctuations, most noticeably in the streamwise component. The model LCS decomposition was used to perform a scale analysis of the data, which was compared to the usual Fourier method. Time intervals of model LCSs were found successively in the data, after subtracting the previous fits. This process resulted in a series of 'levels' with a number of LCSs found at each level. About six levels account for most of the kinetic energy. The model also allows the computation of the Reynolds stress components, for which six levels also are sufficient. The recomposition of the time series on a LCS-by-LCS basis compares well with the mode-by-mode Fourier recomposition for the average momentum fluxes and kinetic energy.