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

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.

• Publication year

  2021

• Venue

  Journal of Fluid Mechanics

• Publication date

  2021-08-27

• Fields of study

  Physics, Engineering

• Identifiers
  DOI 10.1017/jfm.2022.299arXiv 2108.12219
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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