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Turbulence organization, long conceptualized in terms of spatialcoherent-structures, has resisted clear description. A major limitation hasbeen the lack of tools to identify instantaneous spatial organization, whileunravelling the superposition of structures. To address this, we present ageneralized correlation framework, using: (i) correlation measures to identifyinstantaneous vector-field patterns, and (ii) a Helmholtz-decomposition basedstructure-disentanglement paradigm. After examples using canonical flows, weapply these methods to homogeneous isotropic turbulence fields. We show thathigh kinetic energy ($E_k$) regions manifest as interspersed, localized,velocity-jets, contrary to the prevalent view of high $E_k$ regions as largeswirling structures (eddies). High enstrophy ($\omega^2$) regions form smallvorticity-jets, invariably surrounded by swirling-velocity. The jet-like andswirling-velocity structures are spatially exclusive. Decomposing theBiot-Savart contributions from different levels and regions of thevorticity-field reveals the organization of velocity-field structures. High$E_k$ jets are neither self-induced (due to their low vorticity contents), norinduced by strong vorticity, being almost entirely induced, non-locally, by thepermeating intermediate range (rms level) vorticity. High $\omega^2$ swirls,instead, are a superposition of self-induced swirling-velocity along with abackground-induced flow. Moreover, intermediate vorticity dominantly inducesthe velocity-field everywhere. This suggests that turbulence organization couldemerge from non-local and non-linear field interactions, dominated bypermeating intermediate vorticity, leading to an alternative description ofturbulence, contrary to the notion of a strict structural hierarchy. The toolspresented can be readily applied to generic vector and scalar fields associatedwith diverse phenomena.

Correlation and decomposition framework for identifying and  disentangling flow structures: canonical examples and application to  isotropic turbulence