The evolution of sinuous perturbation waves in the turbulent wake of a flat plate is investigated. The Strouhal number of the perturbations is chosen so that the waves remain amplified over the entire range of measurements. Detailed comparisons between linear stability theory and the phase-averaged measurements of the coherent velocity field are presented. Initially, before significant amplification of the perturbation amplitude occurs, the agreement between the linear theory and the measurements is good. The measured amplitude and phase distributions of the streamwise and lateral components of the coherent or wave-induced velocity field as well as the coherent Reynolds stress show excellent agreement with their linear theory counterparts. The coherent Reynolds stress, which is generated through a nonlinear interaction between the fundamental mode and the mean flow, augments the turbulent Reynolds stress causing the spreading rate of the wake to increase. However, this nonlinear interaction does not affect the shape of the mean velocity profile in the early stages of amplification. The linear theory predictions deteriorate with increasing downstream distance because of nonlinearity and the stronger interaction with the turbulent field as the neutral point of the perturbation is approached. For the unforced now, the peak in the measured spectrum of the cross-stream (turbulent) velocity fluctuations at any downstream location (in the far wake) corresponds to the local neutral frequency from linear, spatial stability theory for inviscid, parallel flow.
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