Implication of Taylor's hypothesis on measuring flow modulation

A convective velocity must be specified when using Taylor's frozen eddy hypothesis to relate temporal and spatial fluctuations. Depending on the quantity of interest, using different convective velocities (i.e. time-mean velocity, global convective velocity, etc.) may lead to different conclusions. Often, using Taylor's hypothesis, the relation between temporal and spatial fluctuations is simplified by assuming a temporally averaged velocity as the convection velocity. In flows where turbulence fluctuations are much smaller than the mean flow velocity, the above treatment does not bring in much error (at least for short periods of time). However, when turbulence fluctuations are comparable to the mean velocity, using a constant convective velocity for fluid motions of all scales can sometimes be problematic. In the context of wall-bounded flows, turbulence fluctuations are comparable to the mean flow in the near-wall region, and as a result, using a constant global convective velocity for converting temporal signals to spatial ones distorts the spatial eddies. Although such distortion will not significantly affect measurements of flow quantities including central moments and power spectra, the significance of amplitude modulation is largely overestimated. Here, we show that if temporal hot-wire data are to be used for studying spatial amplitude modulation, the local fluid velocity must be used as the local convective velocity. The impact of amplitude modulation on power spectra and skewness are reconsidered using the proposed correction.