Conversion of Measured Turbulence Spectra from Temporal to Spatial Domain

Abstract

A novel type of conversion of point-measured temporal turbulence power spectra to wavenumber space is proposed. By converting the temporal measurement records into spatial connected streakline elements, the classical assumption of a local mean velocity in Taylor’s hypothesis can be completely bypassed. The presented method is illustrated with examples from both hot-wire anemometry and laser Doppler velocimetry, but may in principle just as well be applied to any flow field property such as pressure, temperature, concentration, or density. Computer generated data of a large eddy with a sharp modulation frequency as well as a turbulent von Karman spectrum are presented to demonstrate the correctness of the principle. Laser Doppler velocimetry measurements, which in themselves appear to be particularly suitable for application of this technique, taken at different off-center positions in a round turbulent jet are then used to demonstrate the difference between the current and the classical temporal-to-spatial domain conversions. The novel method displays the behavior expected from spatial spectra measured along homogeneous directions in the very same turbulent axisymmetric jet, while the classical Taylor’s hypothesis, as expected, shows increasing deviation further away from the center axis where the turbulence intensity grows rapidly. Interpretation of first-order statistics as well as different kinds of spectral estimates is proposed and discussed.