Turbulent flows are complex multi-scale and chaotic motions that need to be classified into more elementary components, referred to coherent turbulent structures. Such a structure must have temporal coherence, i.e. it must persist in its form for long enough periods that the methods of time-averaged statistics can be applied. Coherent structures are typically studied on very large scales, but can be broken down into more elementary structures with coherent properties of their own, such examples include hairpin vortices. Hairpins and coherent structures have been studied and noticed in data since the 1930s, and have been since cited in thousands of scientific papers and reviews.

Flow visualization experiments, using smoke and dye as tracers, have been historically used to simulate coherent structures and verify theories, but computer models are now the dominant tools widely used in the field to verify and understand the formation, evolution, and other properties of such structures. The kinematic properties of these motions include size, scale, shape, vorticity, energy, and the dynamic properties govern the way coherent structures grow, evolve, and decay. Most coherent structures are studied only within the confined forms of simple wall turbulence, which approximates the coherence to be steady, fully developed, incompressible, and with a zero pressure gradient in the boundary layer. Although such approximations depart from reality, they contain sufficient parameters needed to understand turbulent coherent structures in a highly conceptual degree.

The presence of organized motions and structures in turbulent shear flows was apparent for a long time, and has been additionally implied by mixing length hypothesis even before the concept was explicitly stated in literature. There were also early correlation data found by measuring jets and turbulent wakes, particularly by Corrsin and Roshko. Hama's hydrogen bubble technique, which used flow visualization to observe the structures, received wide spread attention and many researchers followed up including Kline. Flow visualization is a laboratory experimental technique that is used to visualize and understand the structures of turbulent shear flows. With a much better understanding of coherent structures, it is now possible to discover and recognize many coherent structures in previous flow-visualization pictures collected of various turbulent flows taken decades ago. Computer simulations are now being the dominant tool for understanding and visualizing coherent flow structures. The ability to compute the necessary time-dependent Navier–Stokes equations produces graphic presentations at a much more sophisticated level, and can additionally be visualized at different planes and resolutions, exceeding the expected sizes and speeds previously generated in laboratory experiments. However, controlled flow visualization experiments are still necessary to direct, develop, and validate the numerical simulations now dominant in the field.

A turbulent flow is a flow regime in fluid dynamics where fluid velocity varies significantly and irregularly in both position and time. Furthermore, a coherent structure is defined as a turbulent flow whose vorticity expression, which is usually stochastic, contains orderly components that can be described as being instantaneously coherent over the spatial extent of the flow structure. In other words, underlying the three-dimensional chaotic vorticity expressions typical of turbulent flows, there is an organized component of that vorticity which is phase-correlated over the entire space of the structure. The instantaneously space and phase correlated vorticity found within the coherent structure expressions can be defined as coherent vorticity, hence making coherent vorticity the main characteristic identifier for coherent structures. Another characteristic inherent in turbulent flows is their intermittency, but intermittency is a very poor identifier of the boundaries of a coherent structure, hence it is generally accepted that the best way to characterize the boundary of a structure is by identifying and defining the boundary of the coherent vorticity.

By defining and identifying coherent structure in this manner, turbulent flows can be decomposed into coherent structures and incoherent structures depending on their coherence, particularly their correlations with their vorticity. Hence, similarly organized events in an ensemble average of organized events can be defined as a coherent structure, and whatever events not identified as similar or phase and space aligned in the ensemble average is an incoherent turbulent structure.

Other attempts at defining a coherent structure can be done through examining the correlation between their momenta or pressure and their turbulent flows. However, it often leads to false indications of turbulence, since pressure and velocity fluctuations over a fluid could be well correlated in the absence of any turbulence or vorticity. Some coherent structures, such as vortex rings, etc. can be large-scale motions comparable to the extent of the shear flow. There are also coherent motions at much smaller scales such as hairpin vortices and typical eddies, which are typically known as coherent substructures, as in coherent structures which can be broken up into smaller more elementary substructures.

Although a coherent structure is by definition characterized by high levels of coherent vorticity, Reynolds stress, production, and heat and mass transportation, it does not necessarily require a high level of kinetic energy. In fact, one of the main roles of coherent structures is the large-scale transport of mass, heat, and momentum without requiring the high amounts of energy normally needed. Consequently, this implies that coherent structures are not the main production and cause of Reynolds stress, and incoherent turbulence can be similarly significant.

Coherent structures cannot superimpose, i.e. they cannot overlap and each coherent structure has its own independent domain and boundary. Since eddies coexist as spatial superpositions, a coherent structure is not an eddy. For example, eddies dissipate energy by obtaining energy from the mean flow at large scales, and eventually dissipating it at the smallest scales. There is no such analogous exchange of energy between coherent structures, and any interaction such as tearing between coherent structures simply results in a new structure. However, two coherent structures can interact and influence each other. The mass of a structure change with time, with the typical case being that structures increase in volume via the diffusion of vorticity.