Doppler effect

The observation of turbulence in the Florida Current is presented with the use of velocity measurements collected with an Acoustic Doppler Current Profiler (ADCP). The research is conducted through application of the theories of Taylor and Kolmogorov and related derivations, and processing tools of MATLAB software to this Eulerian observation of flow [1]. The velocity profile of the Florida Current is deduced in terms of its turbulent character with shear, acceleration, gradient, Reynolds Number, Reynolds Stress, Welch power spectrum density of current velocity, wavenumbers of Taylor’s hypothesis and Kolmogorov, wavenumber spectrum, eddy diameters, diapycnal diffusivity, and the Richardson Number. Processing methods are validated with results of other research conducted in the Florida Current with the use of a Multi-Scale Profiler, and an Advanced Microstructure Profiler for determination of shear, dissipation, diffusivity, and estimates of turbulent eddy diameters based on Taylor’s Hypothesis [1][4]. A spectral analysis is developed and is compared with Kolmogorov’s -5/3-Law. The process and the results of the analysis are described.

When acoustic measurements of moving vehicles are made by a stationary observer, the Doppler shift has two detrimental effects on the interpretation of the data. The spectra are smeared by the change in Doppler factor during the vehicle pass by, and the motion induced phase shift in the signals causes errors. The measured signals can be corrected back to source time if a moving time delay correction is applied. However, when the signals are sampled digitally this time delay correction requires an estimate to be made of the signal level between samples. This can be achieved by using a digital filter with time varying coefficients which estimates the signal from at least two adjacent samples. Results of both numerical simulations and real applications of this technique will be given.

An exactly solvable model is constructed of amplification
of a coherent optical pulse in the extreme Doppler limit.
The pulse so obtained exhibits the expected evolution
toward a pi pulse with pulse amplification and compression,
but differs from the pulse analyzed previously by G. L.
Lamb in that it possesses a continuous leading edge.