Study of the instability of the Poiseuille flow using a thermodynamic formalism

Abstract

The stability of Poiseuille flow is among the most classical problems in fluid mechanics going back to the pioneering work of Reynolds. Despite a huge amount of effort, particularly recent advances in experimental studies, we still lack a suitable theoretical framework. In this paper, we develop a thermodynamic formalism for studying this problem. We show that this formalism allows us to identify a unique critical Reynolds number at which the laminar flow loses stability. We also study the free energy, action, and other thermodynamic relations for the macroscopic quantities associated with the flow. The formalism developed here should be applicable to a large class of problems exhibiting subcritical instabilities.

Document Details

Document Type
Pub Defense Publication
Publication Date
Jul 20, 2015
Source ID
10.1073/pnas.1501288112

Entities

People

  • Jianchun Wang
  • Qianxiao Li
  • Weinan E

Organizations

  • Agency for Science, Technology and Research
  • National Natural Science Foundation of China
  • Office of Naval Research
  • Peking University
  • Princeton University

Tags

Fields of Study

  • Physics

Readers

  • Fluid Dynamics.
  • Plasma Physics / Magnetohydrodynamics
  • Systems Analysis and Design