Stochastic model theory for coherent turbulent structures in circular jets

A stochastic model based on a linearized theory is developed. It is assumed that the large scale structure of the turbulence is created randomly at the jet orifice and that its subsequent convection downstream may be described in terms of quantities predicted by a linearized inviscid stability theory for slowly diverging flows. The process of the generation of turbulence is modeled by the imposition of a stochastic initial condition for the corresponding stability problem. The application of this condition secures the homogeneity of mean values of the turbulent quantities with respect to the angular coordinate; the contribution of each spiral mode is then proportional to a certain spectral function, the latter being an unknown function within the framework of the present study. Since experiments have shown that the turbulence of jets is far from being adequately represented by white noise conditions, the spectral functions must be determined by fitting to experimental data. It is shown that the model is capable of predicting the experimental trends for circumferential and radial coherence functions fairly well. However, complications arise with respect to the axial coherence functions and an attempt is made to alleviate the difficulties by either a cutoff assumption or by a process of continuation of the inviscid quantities.