Koopman analysis of the long-term evolution in a turbulent convection cell

Dimitrios Giannakis, Anastasiya Kolchinskaya, Dmitry Krasnov, Jörg Schumacher

Research output: Contribution to journalReview articlepeer-review


We analyse the long-time evolution of the three-dimensional flow in a closed cubic turbulent Rayleigh-Bénard convection cell via a Koopman eigenfunction analysis. A data-driven basis derived from diffusion kernels known in machine learning is employed here to represent a regularized generator of the unitary Koopman group in the sense of a Galerkin approximation. The resulting Koopman eigenfunctions can be grouped into subsets in accordance with the discrete symmetries in a cubic box. In particular, a projection of the velocity field onto the first group of eigenfunctions reveals the four stable large-scale circulation (LSC) states in the convection cell. We recapture the preferential circulation rolls in diagonal corners and the short-term switching through roll states parallel to the side faces which have also been seen in other simulations and experiments. The diagonal macroscopic flow states can last as long as 1000 convective free-fall time units. In addition, we find that specific pairs of Koopman eigenfunctions in the secondary subset obey enhanced oscillatory fluctuations for particular stable diagonal states of the LSC. The corresponding velocity-field structures, such as corner vortices and swirls in the midplane, are also discussed via spatiotemporal reconstructions.

Original languageEnglish (US)
Pages (from-to)735-767
Number of pages33
JournalJournal of Fluid Mechanics
StatePublished - Jul 25 2018


  • Bénard convection
  • low-dimensional models
  • turbulent convection

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


Dive into the research topics of 'Koopman analysis of the long-term evolution in a turbulent convection cell'. Together they form a unique fingerprint.

Cite this