Book Description

The existence of organized structures in turbulent shear flow has been the subject of recent observational discoveries in both the laboratory and in the atmosphere and ocean. The resent work on modeling such structures in a temporally developing, horizontally homogeneous turbulent free shear layer has been extended to the spatially developing mixing layer, there being no available rational transformation between the two nonlinear problems. The basis for the consideration is the kinetic energy development of the mean flow, large-scale structure and fine-grained turbulence with a conditional average, supplementing the usual time average, to separate the nonrandom from the random part of the fluctuations. The integrated form of the energy equations and the accompanying shape assumptions, is used to derive amplitude equations for the mean flow, characterized by the shear layer thickness, the nonrandom and random components of flow which are characterized by their respective energy densities. In general, the large-scale structure augments the spreading of the shear layer and enhances the fine-grained turbulence by taking energy from the mean flow and transferring it to the turbulence as it amplifies and subsequently decays. The maximal amplitude of the large-scale structure is attained by the initially most amplified mode, however, the relative enhancement of the fine-grained turbulence is achieved by both the magnitude of the large-scale structure and its streamwise lifetime. Thus a greater enhancement of the turbulence is achievable by the lower frequency mdoes which have longer streamwise lifetimes. The large-scale structure can also be controlled by increasing the initial level of turbulence, which would render its decay more rapidly. (Author).