## 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 language | English (US) |
---|---|

Article number | 1409 |

Pages (from-to) | 1409-1440 |

Number of pages | 32 |

Journal | Nonlinearity |

Volume | 28 |

Issue number | 5 |

DOIs | |

State | Published - 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