The Emergence of Characteristic (Coherent?) Motion in Homogeneous Turbulent Shear Flows

In most turbulent flows there exist ‘coherent structures’ (CS) where the velocity and vorticity have a characteristic structures and where the large scale distributions of velocity and vorticity remain coherent — even as the structures move through and interact with the surrounding fluid. There appear to be two distinct approaches to describing coherent structures which reflect the different flows fields in which they occur, viz: (a) Dynamical coherent structures are isolated regions where the vorticity is large and has a characteristic form and which have their own dynamical life and could exist in isolation (Hussain 1986). One approach to analyzing the dynamics of CS is to consider how typical forms of these vortex structures interact with each other and with the ambient shear flow. In the absence of a general theory for covering most kinds of vortex interaction it will be necessary to conduct many such computations to obtain general concepts from them (some aspect of these dynamical interaction were reviewed by Hunt 1987a,b). (b) ‘Kinematic’ coherent structures are regions of characteristic turbulent motion with similar features and similar spatial distributions in all realisations of a particular turbulent flow. Different definitions have been given for these structures based on different properties such as orthogonality, peak velocity, Reynolds stress, strain rate versus vorticity, pressure, etc. (Lumley 1967, Adrian and Moin 1988, Blackwelder and Kaplan 1976, Wray and Hunt 1990). Such a classification has practical aspects, such as the identification of straining and recirculating regions which are significant for mixing, surface deformation, reaction, etc., as well as dynamical aspects, such as the characterisation of production and dissipation regions for energy and enstrophy.