Wavelet Ridges of Wake Instability Modes

Introduction In the dynamics of laminar-turbulent wake transition, it has been established for some time that modulations of the most unstable mode play an important role in the redistribution of spectral energy to other modes (Miksad et al. 1982). In Miksad et al. (1982) the modulations of measured instability modes were obtained with a digital signal analysis technique known as complex demodulation (Kim et al. 1980). This technique is best suited for fluctuations that have a well-defined carrier frequency (i.e. fundamental instability mode) which occurs for transition experiments where acoustic forcing is applied. For the case of natural transition, it has been argued that there is no true carrier frequency (Miksad et al. 1987) and although demodulates were computed for this case using complex demodulation in Miksad et al. (1987), the results were regarded as qualitatively useful but still questionable. The recently developed wavelet transform (Grossman & Morlet, 1984) and subsequent techniques such as wavelet ridge extraction (Mallat, 1998) offer new signal diagnostics for demodulating instability modes, especially for the case when there is no distinct carrier mode. In this paper, we describe an alternative to complex demodulation known as wavelet ridge extraction for measuring modulations in natural transition, determine its frequency response to quantify attenuation characteristics of the technique, and demonstrate its application to a velocity fluctuation measured in the natural transition of a wake.