Budanur, Nazmi BISTA ; Short, Kimberly; Farazmand, Mohammad; Willis, Ashley; Cvitanović, Predrag
The chaotic dynamics of low-dimensional systems, such as Lorenz or Rössler flows, is guided by the infinity of periodic orbits embedded in their strange attractors. Whether this is also the case for the infinite-dimensional dynamics of Navier–Stokes equations has long been speculated, and is a topic of ongoing study. Periodic and relative periodic solutions have been shown to be involved in transitions to turbulence. Their relevance to turbulent dynamics – specifically, whether periodic orbits play the same role in high-dimensional nonlinear systems like the Navier–Stokes equations as they do in lower-dimensional systems – is the focus of the present investigation. We perform here a detailed study of pipe flow relative periodic orbits with energies and mean dissipations close to turbulent values. We outline several approaches to reduction of the translational symmetry of the system. We study pipe flow in a minimal computational cell at Re=2500, and report a library of invariant solutions found with the aid of the method of slices. Detailed study of the unstable manifolds of a sample of these solutions is consistent with the picture that relative periodic orbits are embedded in the chaotic saddle and that they guide the turbulent dynamics.
Journal of Fluid Mechanics
274 - 301
Budanur NB, Short K, Farazmand M, Willis A, Cvitanović P. Relative periodic orbits form the backbone of turbulent pipe flow. Journal of Fluid Mechanics. 2017;833:274-301. doi:10.1017/jfm.2017.699
Budanur, N. B., Short, K., Farazmand, M., Willis, A., & Cvitanović, P. (2017). Relative periodic orbits form the backbone of turbulent pipe flow. Journal of Fluid Mechanics. Cambridge University Press. https://doi.org/10.1017/jfm.2017.699
Budanur, Nazmi B, Kimberly Short, Mohammad Farazmand, Ashley Willis, and Predrag Cvitanović. “Relative Periodic Orbits Form the Backbone of Turbulent Pipe Flow.” Journal of Fluid Mechanics. Cambridge University Press, 2017. https://doi.org/10.1017/jfm.2017.699.
N. B. Budanur, K. Short, M. Farazmand, A. Willis, and P. Cvitanović, “Relative periodic orbits form the backbone of turbulent pipe flow,” Journal of Fluid Mechanics, vol. 833. Cambridge University Press, pp. 274–301, 2017.
Budanur NB, Short K, Farazmand M, Willis A, Cvitanović P. 2017. Relative periodic orbits form the backbone of turbulent pipe flow. Journal of Fluid Mechanics. 833, 274–301.
Budanur, Nazmi B., et al. “Relative Periodic Orbits Form the Backbone of Turbulent Pipe Flow.” Journal of Fluid Mechanics, vol. 833, Cambridge University Press, 2017, pp. 274–301, doi:10.1017/jfm.2017.699.