Coherent turbulent structure
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.
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.
Although such approximations depart from reality, they contain sufficient parameters needed to understand turbulent coherent structures in a highly conceptual degree.
[2] 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.
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.
Other attempts at defining a coherent structure can be done through examining the correlation between their momenta or pressure and their turbulent flows.
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.
The next most significant measures include contoured depictions of coherent strain rate and shear production.
These measures of initial flow conditions can be organized and grouped into three broad categories: laminar, highly disturbed, and fully turbulent.
Lagrangian coherent structures (LCSs) are influential material surfaces that create clearly recognizable patterns in passive tracer distributions advected by an unsteady flow.
These surfaces are generalizations of classical invariant manifolds, known in dynamical systems theory, to finite-time unsteady flow data.
Various mathematical techniques have been developed to identify LCSs in two- and three-dimenisonal data sets, and have been applied to laboratory experiments, numerical simulations and geophysical observations.
The hairpin-shaped vortices are believed to be one of the most important and elementary sustained flow patterns in turbulent boundary layers.
Hence, such eruptions are a regenerative process, in which they act to create vortices near the surface and eject them out onto the outer regions of the turbulent wall.
During the production of this Reynold's stress term, the contributions come in sharp intermittent time segments when eruptions bring new vortices outward.
Theodorsen has been producing sketches that indicate the presence of hairpin vortices in his flow visualization experiments.
[1] Since the mass usage of computers, direct numerical simulations or DNS have been used widely, producing vast data sets describing the complex evolution of flow.
Researchers look around this region of high shear for indications of individual vortex structures based on accepted definitions, like coherent vortices.
