Wednesday, September 23 2020
15:30 - 16:30

IMSc Webinar

Exploring Turbulence using Exact Coherent States

Balachandra Suri

Institute of Science \& Technology (IST), Austria

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Turbulence is widely regarded as the last unsolved problem of classical physics. Despite the availability of well-defined governing equations, a tractable framework that predicts the dynamical and statistical properties of turbulence has eluded scientists. In this talk, we discuss how unstable nonchaotic solutions of the Navier-Stokes equation, called Exact Coherent States (ECS), may prove pivotal in developing such a framework. Specifically, we focus on moderately turbulent (quasi-two-dimensional) flows, which are characterized by the fleeting appearance of well-discernible flow patterns called coherent structures. We show that the appearance of coherent structures is related to the dynamical significance of ECS, such as equilibrium or time-periodic flows. Using these special solutions, we then construct a low-dimensional model for flow evolution and forecast turbulence for a short duration. Analyzing their statistical significance, we also show that frequently appearing ECS capture statistical averages (e.g., rate of energy dissipation) of turbulent flows accurately. Finally, we discuss how a network of dynamical connections between ECSs constrains long-term flow dynamics and provides a tractable deterministic picture of turbulence.

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