IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Numerical Study of the Global Stability of Plane Poiseuille Flow

  • April 7, 2014
  • 1 p.m.
  • LeConte 312

Abstract

The instability of pipe flow was first examined by Osborne Reynolds in 1883. Since then, the instability of fluid dynamics became one of the most important challenges in Physics and Mathematics. The linear stability analysis was first introduced by W. M. Orr and A. Sommerfeld (1907,1908). Later, a lot of theoretical and numerical works were carried out for the linear stability analysis. However, linear stability analysis is not sufficient for the instability of nonlinear Navier-Stokes equation. This has been one of the most important problems in fluid dynamics for more than one century. In this talk, we introduce two methods to study the global stability of solutions of plane shear flow. The first one is the Minimum Action Method (MAM), it is a deterministic method minimizing the action on the transition path. The second method is a stochastic method, which study the global stability by solving the stochastic Navier-Stokes equation for a very very long time. Both approaches require huge computations, therefore spectral methods are used to reduce the degree of freedom and overall computational cost. The numerical results show that the steady state plane Poiseuille flow become unstable when Reynolds number exceed a threshold about 2500. This is a joint work with Prof. Weinan E and Xiaoliang Wan.

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