Geometric decomposition of the conformation tensor in viscoelastic turbulence

Abstract

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

arXiv comment32 pages, 10 figures

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• On the large-Weissenberg-number scaling laws in viscoelastic pipe flows
• Vorticity dynamics and drag for flows over a sphere and a prolate spheroid
• Experimental observation of the origin and structure of elasto-inertial turbulence
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• Uncertainty in Elastic Turbulence
• Polymer stretching in laminar and random flows: entropic characterization
• Perturbation symmetries in shear-thinning viscoelastic pipe flows and the Petrov-Galerkin implementation
• Vorticity amplification in viscoelastic channel flows with long-wave surface distortions