A study of the interactions between large-scale coherent structures and fine-grained turbulence in a round jet

An approximate energy integral description is used to study the development of large-scale coherent structures in the technologically important problem of the round turbulent jet. The analysis begins from the radially integrated form of the kinetic energy equations of the mean flow, the large-scale structure and the fine-grained turbulence, which are obtained by using the usual Reynolds time average and a conditional average with reference to the frequency of the idealized monochromatic component of the large-scale wavelike structure. This is the basis for obtaining the amplitude equations for the three components of the flow in terms of the mean flow momentum thickness, the large-scale structure kinetic energy and the fine-grained turbulence kinetic energy across the jet.