Budanur, N.B., Marensi, E. orcid.org/0000-0001-7173-4923, Willis, A.P. orcid.org/0000-0002-2693-2952 et al. (1 more author) (2020) Upper edge of chaos and the energetics of transition in pipe flow. Physical Review Fluids, 5 (2). 023903. ISSN 2469-990X
Abstract
In the past two decades, our understanding of the transition to turbulence in shear flows with linearly stable laminar solutions has greatly improved. Regarding the susceptibility of the laminar flow, two concepts have been particularly useful: the edge states and the minimal seeds. In this nonlinear picture of the transition, the basin boundary of turbulence is set by the edge state's stable manifold and this manifold comes closest in energy to the laminar equilibrium at the minimal seed. We begin this paper by presenting numerical experiments in which three-dimensional perturbations are too energetic to trigger turbulence in pipe flow but they do lead to turbulence when their amplitude is reduced. We show that this seemingly counter-intuitive observation is in fact consistent with the fully nonlinear description of the transition mediated by the edge state. In order to understand the physical mechanisms behind this process, we measure the turbulent kinetic energy production and dissipation rates as a function of the radial coordinate. Our main observation is that the transition to turbulence relies on the energy amplification away from the wall, as opposed to the turbulence itself, whose energy is predominantly produced near the wall. This observation is further supported by the similar analyses on the minimal seeds and the edge states. Furthermore, we show that the time-evolution of production-over-dissipation curves provide a clear distinction between the different initial amplification stages of the transition to turbulence from the minimal seed.
Metadata
Item Type: | Article |
---|---|
Authors/Creators: |
|
Copyright, Publisher and Additional Information: | © 2020 American Physical Society. This is an author-produced version of a paper subsequently published in Physical Review Fluids. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | physics.flu-dyn; physics.flu-dyn; nlin.CD |
Dates: |
|
Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Funding Information: | Funder Grant number Engineering and Physical Science Research Council EP/P000959/1 |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 17 Jan 2020 12:27 |
Last Modified: | 01 Dec 2020 11:29 |
Status: | Published |
Publisher: | American Physical Society |
Refereed: | Yes |
Identification Number: | 10.1103/PhysRevFluids.5.023903 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:155040 |