Heteroclinic and Homoclinic Connections in a Kolmogorov-Like Flow
Abstract
Recent studies suggest that unstable recurrent solutions of the Navier-Stokes equation provide new insights into dynamics of turbulent flows. In this study, we compute an extensive network of dynamical connections between such solutions in a weakly turbulent quasi-two-dimensional Kolmogorov flow that lies in the inversion-symmetric subspace. In particular, we find numerous isolated heteroclinic connections between different types of solutions - equilibria, periodic, and quasi-periodic orbits - as well as continua of connections forming higher-dimensional connecting manifolds. We also compute a homoclinic connection of a periodic orbit and provide strong evidence that the associated homoclinic tangle forms the chaotic repeller that underpins transient turbulence in the symmetric subspace.
National Science Foundation Grants: CMMI-1234436, DMS-1125302, CMMI-1725587. Defense Advanced Research Projects Agency Grant HR0011-16-2-0033.- Publication:
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APS Division of Fluid Dynamics Meeting Abstracts
- Pub Date:
- November 2019
- Bibcode:
- 2019APS..DFDC11003S