Taylor hypothesis and large-scale coherent structures

Abstract

The applicability of the Taylor hypothesis to large-scale coherent structures in turbulent shear flows has been evaluated by comparing the actual spatial distributions of the structure properties with those deduced through the use of the hypothesis. This study has been carried out in the near field of a 7[sdot ]62 cm circular air jet at a jet Reynolds number of 3[sdot ]2 x 10⁴, where the coherent structures and their interactions have been organized through controlled excitation. Actual distributions of the structure properties have been obtained through phase-average hot-wire data, the measurements having been repeated at different spatial points over the extents of the structure crosssections at a fixed phase. The corresponding ‘spatial’ distributions of these properties obtained (by using the Taylor hypothesis) from the temporal data at appropriate phases and locations, show that the hypothesis works quite well for an isolated coherent structure if a constant convection velocity, equal to the structure centre velocity, is used in the hypothesis everywhere across the shear flow. The popular use of the local time-average or even the instantaneous streamwise velocity produces unacceptably large distortions. When structure interactions like pairing are involved, no convection velocity can be found with which the hypothesis works. Distributions of the terms in the Navier–Stokes equation contributing to the phase-average vorticity, but neglected by the hypothesis, have been quantitatively determined. These show that the terms associated with the background turbulence field, but not those associated with the coherent motion field, can be neglected. In particular, the pressure term due to the coherent motion field is large and cannot be neglected.