Model the nonlinear instability of wall-bounded shear flows as a rare event: A study on two-dimensional Poiseuille flow

Xiaoliang Wan, Haijun Yu, E. Weinan

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In this work, we study the nonlinear instability of two-dimensional (2D) wall-bounded shear flows from the large deviation point of view. The main idea is to consider the Navier-Stokes equations perturbed by small noise in force and then examine the noise-induced transitions between the two coexisting stable solutions due to the subcritical bifurcation. When the amplitude of the noise goes to zero, the Freidlin-Wentzell (F-W) theory of large deviations defines the most probable transition path in the phase space, which is the minimizer of the F-W action functional and characterizes the development of the nonlinear instability subject to small random perturbations. Based on such a transition path we can define a critical Reynolds number for the nonlinear instability in the probabilistic sense. Then the action-based stability theory is applied to study the 2D Poiseuille flow in a short channel.

Original languageEnglish (US)
Article number1409
Pages (from-to)1409-1440
Number of pages32
JournalNonlinearity
Volume28
Issue number5
DOIs
StatePublished - May 1 2015

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

Keywords

  • hydrodynamic stability
  • large deviation theory
  • minimum action method

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