Application of the continuous wavelet transform to science and engineering problems: Fluid dynamics case studies

The continuous wavelet transform is demonstrated to be a versatile tool for the analysis of fluctuation phenomena which exhibit transient or intermittent/random frequency content. In particular, the capabilities of the continuous wavelet transform for obtaining quantitative measures of fluctuation characteristics are demonstrated through its application to three fluid dynamics problems which are representative of general problems involving transient dynamic response, time-localized input-output relationships and measurement of the composition of time-localized fluctuations. A continuous wavelet transform implementation procedure for digital analysis of sampled fluctuations is developed and numerous test signals are used to verify and interpret wavelet analysis results. Wavelet-based signal diagnostics are applied, and in some cases developed, to achieve specific analysis objectives which are derived from the primary objectives of the individual fluid dynamics problems.;It is first shown that the continuous wavelet transform serves as a versatile tool for the extraction of time-dependent modal amplitudes of multiple sinusoidal response modes and can be readily extended to handle cases such as transient random response. The specific fluid dynamics problem used to demonstrate wavelet analysis of transient response is the characterization of the transients in the surge response of spar platforms due to ocean wave excitation. In the next problem, the analysis of time-localized input-output relationships, it is shown that the cross scalogram and the wavelet energy spectrum of individual events have utility for elucidating the nature of time-localized input-output relationships between two simultaneously measured fluctuations. The wavelet analysis of time-localized input-output relationships is demonstrated by examining the relationship between turbulent velocity fluctuations in the atmospheric surface layer and pressure peaks on low-rise structures. Finally, it is shown that the continuous wavelet transform can be used to measure the composition (scale content and its corresponding energy) of time-localized fluctuations. The utility of the wavelet transform for the analysis of time-localized fluctuations is demonstrated with the analysis of large scale intermittent ‘events’ which are observed in the measured velocity fluctuations of a wake undergoing transition to turbulence.