Over the past decade, the edge of chaos has proven to be a fruitful starting point for investigations of shear flows when the laminar base flow is linearly stable. Numerous computational studies of shear flows demonstrated the existence of states that separate laminar and turbulent regions of the state space. In addition, some studies determined invariant solutions that reside on this edge. In this paper, we study the unstable manifold of one such solution with the aid of continuous symmetry reduction, which we formulate here for the simultaneous quotiening of axial and azimuthal symmetries. Upon our investigation of the unstable manifold, we discover a previously unknown traveling-wave solution on the laminar-turbulent boundary with a relatively complex structure. By means of low-dimensional projections, we visualize different dynamical paths that connect these solutions to the turbulence. Our numerical experiments demonstrate that the laminar-turbulent boundary exhibits qualitatively different regions whose properties are influenced by the nearby invariant solutions.
Physical Review Fluids
Budanur NB, Hof B. Complexity of the laminar-turbulent boundary in pipe flow. Physical Review Fluids. 2018;3(5). doi:10.1103/PhysRevFluids.3.054401
Budanur, N. B., & Hof, B. (2018). Complexity of the laminar-turbulent boundary in pipe flow. Physical Review Fluids. American Physical Society. https://doi.org/10.1103/PhysRevFluids.3.054401
Budanur, Nazmi B, and Björn Hof. “Complexity of the Laminar-Turbulent Boundary in Pipe Flow.” Physical Review Fluids. American Physical Society, 2018. https://doi.org/10.1103/PhysRevFluids.3.054401.
N. B. Budanur and B. Hof, “Complexity of the laminar-turbulent boundary in pipe flow,” Physical Review Fluids, vol. 3, no. 5. American Physical Society, 2018.
Budanur NB, Hof B. 2018. Complexity of the laminar-turbulent boundary in pipe flow. Physical Review Fluids. 3(5), 054401.
Budanur, Nazmi B., and Björn Hof. “Complexity of the Laminar-Turbulent Boundary in Pipe Flow.” Physical Review Fluids, vol. 3, no. 5, 054401, American Physical Society, 2018, doi:10.1103/PhysRevFluids.3.054401.