Stable Manifolds and the Transition to Turbulence in Pipe Flow
Fluid Dynamics
2015-05-13 v2
Abstract
Lower-branch traveling waves and equilibria computed in pipe flow and other shear flows appear intermediate between turbulent and laminar motions. We take a step towards connecting these lower-branch solutions to transition by deriving a numerical method for finding certain special disturbances of the laminar flow in a short pipe. These special disturbances cause the disturbed velocity field to approach the lower-branch solution by evolving along its stable manifold. If the disturbance were slightly smaller, the flow would relaminarize, and if slightly larger, it would transition to a turbulent state.
Cite
@article{arxiv.0801.1918,
title = {Stable Manifolds and the Transition to Turbulence in Pipe Flow},
author = {D. Viswanath and P. Cvitanovic},
journal= {arXiv preprint arXiv:0801.1918},
year = {2015}
}