Unstable manifold computations for the two-dimensional plane Poiseuille flow |
| |
Authors: | Pablo S. Casas Àngel Jorba |
| |
Affiliation: | (1) Departamento de Matemática Aplicada I, Universidad Politécnica de Cataluña, Diagonal, 647, 08028 Barcelona, Spain;(2) Departamento de Matemática Aplicada y Análisis, Universidad de Barcelona, Gran Via, 585, 08007 Barcelona, Spain |
| |
Abstract: | We follow the unstable manifold of periodic and quasi-periodic solutions in time for the Poiseuille problem, using two formulations: holding a constant flux or mean pressure gradient. By means of a numerical integrator of the Navier–Stokes equations, we let the fluid evolve from an initially perturbed unstable solution until the fluid reaches an attracting state. Thus, we detect several connections among different configurations of the flow such as laminar, periodic, quasi-periodic with two or three basic frequencies, and more complex sets that we have not been able to classify. These connections make possible the location of new families of solutions, usually hard to find by means of numerical continuation of curves, and show the richness of the dynamics of the Poiseuille flow. PACS 05.45.-a, 47.11.+j, 47.20.-k, 47.20.Ft |
| |
Keywords: | incompressible Navier– Stokes equation direct numerical simulation nonlinear dynamical systems |
本文献已被 SpringerLink 等数据库收录! |
|