Orthonormal wavelet decomposition of turbulent flows: intermittency and coherent structures

Abstract

Experimental data obtained in various turbulent flows are analysed by means of orthogonal wavelet transforms. Several configurations are analysed: homogeneous grid turbulence at low and very low Re_λ, and fully developed jet turbulence at moderate and high Re_λ. It is shown by means of the wavelet decomposition in combination with the form of scaling named extended self-similarity that some statistical properties of fully developed turbulence may be extended to low-Re_λ flows. Indeed, universal properties related to intermittency are observed down to Re_λ≃10. Furthermore, the use of a new conditional averaging technique of velocity signals, based on the wavelet transform, permits the identification of the time signatures of coherent structures which may or may not be responsible for intermittency depending on the scale of the structure itself. It is shown that in grid turbulence, intermittency at the smallest scales is related to structures with small characteristic size and with a shape that may be related to the passage of vortex tubes. In jet turbulence, the longitudinal velocity component reveals that intermittency may be induced by structures with a size of the order of the integral length. This effect is interpreted as the signature of the characteristic jet mixing layer structures. The structures identified on the transverse velocity component of the jet case turn out on the other hand not to be affected by the mixing layer and the corresponding shape is again correlated with the signature of vortex tubes.