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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Coherent turbulent structure | 2/3 | https://en.wikipedia.org/wiki/Coherent_turbulent_structure | reference | science, encyclopedia | 2026-05-05T13:41:38.365090+00:00 | kb-cron |
== Characteristics == 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. One of the most fundamental quantities of coherent structures is characterized by coherent vorticity,
Ω
c
{\displaystyle \Omega _{c}}
. Perhaps the next most critical measures of coherent structures are the coherent vs. incoherent Reynold's stresses,
−
u
c
ν
c
{\displaystyle -u_{c}\nu _{c}}
and
−
⟨
u
r
ν
r
⟩
{\displaystyle -\langle u_{r}\nu _{r}\rangle }
. These represent the transports of momentum, and their relative strength indicates how much momentum is being transported by coherent structures as compared to incoherent structures. The next most significant measures include contoured depictions of coherent strain rate and shear production. A useful property of such contours is that they are invariant under Galilean transformations, hence the contours of coherent vorticity constitute an excellent identifier to the structure's boundaries. The contours of these properties not only locate where exactly coherent structure quantities have their peaks and saddles, but also identify where the incoherent turbulent structures are when overlaid on their directional gradients. In addition, spatial contours can be drawn describe the shape, size, and strength of the coherent structures, depicting not only the mechanics but also the dynamical evolution of coherent structures. For example, in order for a structure to be evolving, and hence dominant, its coherent vorticity, coherent Reynolds stress, and production terms should be larger than the time averaged values of the flow structures.
== Formation == Coherent structures form due to some sort of instability, e.g. the Kelvin–Helmholtz instability. Identifying an instability, and hence the initial formation of a coherent structure, requires the knowledge of initial conditions of the flow structure. Hence, documentation of the initial condition is essential for capturing the evolution and interactions of coherent structures, since initial conditions are quite variable. Overlooking the initial conditions was common in early studies due to researchers overlooking their significance. Initial conditions include the mean velocity profile, thickness, shape, the probability densities of velocity and momentum, the spectrum of Reynolds stress values, etc. These measures of initial flow conditions can be organized and grouped into three broad categories: laminar, highly disturbed, and fully turbulent. Out of the three categories, coherent structures typically arise from instabilities in laminar or turbulent states. After an initial triggering, their growth is determined by evolutionary changes due to non-linear interactions with other coherent structures, or their decay onto incoherent turbulent structures. Observed rapid changes lead to the belief that there must be a regenerative cycle that takes place during decay. For example, after a structure decays, the result may be that the flow is now turbulent and becomes susceptible to a new instability determined by the new flow state, leading to a new coherent structure being formed. It is also possible that structures do not decay and instead distort by splitting into substructures or interacting with other coherent structures.
== Categories of coherent structures ==
=== Lagrangian coherent structures ===
Lagrangian coherent structures (LCSs) are influential material surfaces that create clearly recognizable patterns in passive tracer distributions advected by an unsteady flow. LCSs can be classified as hyperbolic (locally maximally attracting or repelling material surfaces), elliptic (material vortex boundaries), and parabolic (material jet cores). These surfaces are generalizations of classical invariant manifolds, known in dynamical systems theory, to finite-time unsteady flow data. This Lagrangian perspective on coherence is concerned with structures formed by fluid elements, as opposed to the Eulerian notion of coherence, which considers features in the instantaneous velocity field of the fluid. Various mathematical techniques have been developed to identify LCSs in two- and three-dimensional data sets, and have been applied to laboratory experiments, numerical simulations and geophysical observations.