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arXiv · 1602.04904

Fluid Stretching as a Levy Process

Marco Dentz·Daniel R. Lester·Tanguy Le Borgne·Felipe P. J. de Barros
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Abstract

We study the relation between flow structure and fluid deformation in steady two-dimensional random flows. Beyond the linear (shear flow) and exponential (chaotic flow) elongation paradigms, we find a broad spectrum of stretching behaviors, ranging from sub- to superlinear, which are dominated by intermittent shear events. We analyze these behaviors from first principles, which uncovers stretching as a result of the non-linear coupling between Lagrangian shear deformation and velocity fluctuations along streamlines. We derive explicit expressions for Lagrangian deformation and demonstrate that stretching obeys a coupled continous time random walk, which for broad distributions of flow velocities describes a Lévy walk for elongation. The derived model provides a direct link between the flow and deformation statistics, and a natural way to quantify the impact of intermittent shear events on the stretching behavior, which can have strong anomalous diffusive character.

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Marco Dentz, Daniel R. Lester, Tanguy Le Borgne, Felipe P. J. de Barros. 2016-08-24. Fluid Stretching as a Levy Process. https://arxiv.org/abs/1602.04904

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