Spatial Spectrum From Particle Image Velocimetry Data

We present a simple method of obtaining the turbulence kinetic energy spectrum from spatially resolved particle image velocimetry (PIV) data without need of use of Taylor hypothesis of frozen turbulence. Additionally, this method allows us to extract the velocity field components related to individual length scales resolved in the spectrum. We convolute the measured PIV velocity field with a band-pass filter, i.e., a difference of two Gauss functions with different widths, and the energy content of a such product we relate to the relevant length-scale of the used band. This is a “kind of wavelet transformation”, which, in respect to Fourier transformation, gives a good physical meaning to individual components.