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arXiv · 2108.12219

Variational methods for finding periodic orbits in the incompressible Navier-Stokes equations

Jeremy P Parker·Tobias M Schneider
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Abstract

Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier-Stokes equations, based on variations of an integral objective functional, and using traditional gradient-based optimisation strategies. Different approaches for handling the incompressibility condition are considered. The variational methods are applied to the specific case of periodic, two-dimensional Kolmogorov flow and compared against existing Newton iteration-based shooting methods. While computationally slow, our methods converge from very inaccurate initial guesses.

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BibTeXRIS

Jeremy P Parker, Tobias M Schneider. 2021-08-27. Variational methods for finding periodic orbits in the incompressible Navier-Stokes equations. https://doi.org/10.1017/jfm.2022.299

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