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

• Published in: arXiv.org
• Main Authors: Mukherjee, Siddhartha, Mascini, Merlijn, Portela, Luis M
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 15.11.2020
• Subjects: Correlation analysis; Decomposition; Fluid dynamics; Isotropic turbulence; Jets; Kinetic energy; Physics - Fluid Dynamics; Scalars; Structural hierarchy; Swirling; Velocity; Vorticity
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2011.07455

Turbulence organization, long conceptualized in terms of spatial coherent-structures, has resisted clear description. A major limitation has been the lack of tools to identify instantaneous spatial organization, while unravelling the superposition of structures. To address this, we present a generalized correlation framework, using: (i) correlation measures to identify instantaneous vector-field patterns, and (ii) a Helmholtz-decomposition based structure-disentanglement paradigm. After examples using canonical flows, we apply these methods to homogeneous isotropic turbulence fields. We show that high kinetic energy (\(E_k\)) regions manifest as interspersed, localized, velocity-jets, contrary to the prevalent view of high \(E_k\) regions as large swirling structures (eddies). High enstrophy (\(\omega^2\)) regions form small vorticity-jets, invariably surrounded by swirling-velocity. The jet-like and swirling-velocity structures are spatially exclusive. Decomposing the Biot-Savart contributions from different levels and regions of the vorticity-field reveals the organization of velocity-field structures. High \(E_k\) jets are neither self-induced (due to their low vorticity contents), nor induced by strong vorticity, being almost entirely induced, non-locally, by the permeating intermediate range (rms level) vorticity. High \(\omega^2\) swirls, instead, are a superposition of self-induced swirling-velocity along with a background-induced flow. Moreover, intermediate vorticity dominantly induces the velocity-field everywhere. This suggests that turbulence organization could emerge from non-local and non-linear field interactions, dominated by permeating intermediate vorticity, leading to an alternative description of turbulence, contrary to the notion of a strict structural hierarchy. The tools presented can be readily applied to generic vector and scalar fields associated with diverse phenomena.