Parker, J. P.Schneider, T. M.2022-05-092022-05-092022-05-092022-04-2610.1017/jfm.2022.299https://infoscience.epfl.ch/handle/20.500.14299/187621WOS:000787325100001Unstable 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.MechanicsPhysics, Fluids & PlasmasPhysicsturbulent flowsnonlinear dynamical systemsinvariant solutionskolmogorovflowtext::journal::journal article::research article