Coherent structures in turbulent flows

Abstract Coherent structures—loosely defined as regions of concentrated vorticity, characteristic and flow-specific organization, recurrence, appreciable lifetime and scale—have been the foremost object of scientific curiosity and dispute in turbulence research for more than ten years past. The concept, based on visual observations, that turbulence, hitherto viewed as a purely random phenomenon, appears to contain a constituent of clearly organized structure promised an alternative to the frustrating verdict that turbulence can only be understood and tackled on statistical grounds. After a first period of enthusiasm, which was then nourished by a few supportive survey papers, the concept was challenged and criticism as to the uniqueness, the ubiquity and finally the importance of those structures was put forward. Although a great number of turbulent flow configurations—essentially all of ‘classical’ flows—have to some extent been investigated and scrutinized for their content of structural organization, many questions remain open and the dispute is by no means settled. In this review we shall restrict ourselves to trying to summarize a few of the more important results and issues without trying to settle this argument. At the same time some open questions will be discussed. Meanwhile an abundance of knowledge has been collected on some free flows, in particular the mixing layer, the wake and—to a lesser extent—the turbulent far jet. All free flows undergo at least one transformation before they become self-similar and unique (do they indeed become unique?). Thus, the mixing layer is the eventual outcome of the transformation of the boundary layer flow from the nozzle. Jets and wakes in their early stages go through intermediate mixing-layer manifestations. Little wonder that also in those cases we often find more than one characteristic structure. Different structural developments appear to be related to different behaviours of the basic flow: The more complex structures, characterized by three-dimensional (Reynolds number and/or lifetime-dependent) agglomerations of hairpin, ring and spiral vortices as in a spot or a puff, are found in those flows which are primarily frictionally unstable (wall flows). Particularly in the boundary layer, we observe a whole zoo of structures, some of which (e.g. the wall streaks) clearly violate the obviously too limiting ‘classical” definition of coherent structures being exclusively ‘large scale’ events. Consequently, as much as these findings undoubtedly add to our understanding of turbulent processes, the concept of coherent structures forfeits some of its original meaning for a more refined picture, the larger the structural multitude becomes. In those flows where inviscid (inflection-point) instability dominates, we find comparatively simpler structures of large scales like single line or ring vortices as in mixing-layer, jet and wake flows, with three-dimensionalities following secondary instabilities. But also there we find the corresponding ‘small scale structures’, longitudinal vortices along the interconnecting braids between the large-scale structures. The common aspect then for all shear flows seems to be the existence of at least two coherent scales, the small one with longitudinal (stretched) vortices being responsible for turbulence-energy production, while the large scale takes care of part of the diffusion. An independent aspect is introduced by the consideration of spiral turbulence as being an intrinsic feature of turbulence eventually leading to the formation of coherent structures in all three-dimensional flows. Formation of coherent structures, as we observe it, touches on a phenomenon of greater generality and significance: spontaneous formation of organized structures from a state of relative disorder is found in organic as well as in inorganic nature. This process is known as Synergetic, and chaos theory is but one of the theoretical tools of this discipline. It is evident that organized structures could not be observed or educed by methods applying any indiscriminate averaging scheme such as Reynolds-averaging. As a consequence, after existence of those structures was evident from visualization, adequate techniques had to be developed to educe repetitive flow events of a certain similarity. The true fraction of coherent energy in the overall turbulent energy can, however, not possibly be assessed with any claim to accuracy. Estimates (their reliability supported by the fact that different methods give similar numbers) show the coherent structures to be responsible for between 10% and 25% of the turbulent energy in most of the flows considered (contrary to Townsend's “big eddies” whose energy content was assumed to be essentially negligible). This figure emphasizes the importance of coherent structures in correctly modelling turbulent flows and, even more so, as a medium to manipulate turbulence (by mechanical, acoustical or chemical means) and thereby influence its most notable technical consequences: noise, mixing, combustion and drag.