Heteroclinic and homoclinic connections in a Kolmogorov-like flow

B. Suri, R.K. Pallantla, M.F. Schatz, R.O. Grigoriev, Physical Review E 100 (2019) 013112.


Journal Article | Published | English
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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 quasiperiodic 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.
Publishing Year
Date Published
2019-07-25
Journal Title
Physical Review E
Volume
100
Issue
1
Article Number
013112
ISSN
eISSN
IST-REx-ID

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Suri B, Pallantla RK, Schatz MF, Grigoriev RO. Heteroclinic and homoclinic connections in a Kolmogorov-like flow. Physical Review E. 2019;100(1):013112. doi:10.1103/physreve.100.013112
Suri, B., Pallantla, R. K., Schatz, M. F., & Grigoriev, R. O. (2019). Heteroclinic and homoclinic connections in a Kolmogorov-like flow. Physical Review E, 100(1), 013112. https://doi.org/10.1103/physreve.100.013112
Suri, Balachandra, Ravi Kumar Pallantla, Michael F. Schatz, and Roman O. Grigoriev. “Heteroclinic and Homoclinic Connections in a Kolmogorov-like Flow.” Physical Review E 100, no. 1 (2019): 013112. https://doi.org/10.1103/physreve.100.013112.
B. Suri, R. K. Pallantla, M. F. Schatz, and R. O. Grigoriev, “Heteroclinic and homoclinic connections in a Kolmogorov-like flow,” Physical Review E, vol. 100, no. 1, p. 013112, 2019.
Suri B, Pallantla RK, Schatz MF, Grigoriev RO. 2019. Heteroclinic and homoclinic connections in a Kolmogorov-like flow. Physical Review E. 100(1), 013112.
Suri, Balachandra, et al. “Heteroclinic and Homoclinic Connections in a Kolmogorov-like Flow.” Physical Review E, vol. 100, no. 1, APS, 2019, p. 013112, doi:10.1103/physreve.100.013112.

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