CTA Measurement on the Frequency Response of a Grid Turbulence Fluctuation Measurement with a Focus on Bispectrum

The aim of this study is to investigate a triple correlation function and a bispectrum of a turbulent voltage fluctuation obtained by a constant-temperature hot-wire anemometer (CTA) in terms of frequency response adjustment. The triple correlation function of a velocity fluctuation is included in the Kármán-Hawarth equation, which is the governing equation for an autocorrelation function. The bispectrum is obtained by Fourier transforming this triple correlation function. The velocity fluctuations in this experiment are obtained for multi-scale grid turbulence, and time series of these voltage fluctuations are measured by the constant-temperature hot-wire anemometer based on a
$5\mu \mathrm{m}$
tungsten wire I probe. The sampling frequency is
$50\text{kHz}$
and an analogue low-pass filter of
$20\text{kHz}$
is used. Firstly, two cases are set up using a square wave where the frequency response is adjusted or unadjusted and oscillating. The effect of the unadjusted response is seen in the power spectrum of the voltage fluctuations. The distributions of the triple correlation function are then compared with and without this response adjustment. The bispectrum of the voltage fluctuations is then shown to be insensitive to the presence or absence of the response adjustment.