Orthonormal wavelet transformations are used to decompose velocity signals of grid
turbulence into both space and scale. The transforms exhibit small-scale enhancements
of (i) the spatial fluctuation, (ii) the correlation in space between the adjacent scales,
and (iii) the correlation in space between the longitudinal and transverse components.
The spatial fluctuation and the scale–scale correlation at small scales are more
significant in the transverse component than in the longitudinal component. These
features are the same for different families of wavelets.
Turbulence contains tube-like structures of vorticity. We demonstrate that wavelet
transforms of velocities are enhanced at the positions of the tubes, by using a direct
numerical simulation. Thus our wavelet analyses have captured the effects of those
coherent structures on velocities measured in the experiment, which would be difficult
for traditional analysis techniques such as those with velocity increments.