Skip to main content
Article thumbnail
Location of Repository

Convection, stability, and low dimensional dynamics

By Charles R. Doering


Recent developments concerning the connection between notions of hydrodynamic stability—usually associated with stationary laminar flows—and dynamics, most notably turbulent fluid flows, are reviewed. Based on a technical device originally introduced by Hopf in 1941, a rigorous mathematical relationship between criteria for nonlinear energy stability and bounds on global transport by steady, unsteady, or even turbulent flows, has been established. The optimal “marginal stability” criteria for the best bound leads to a novel variational problem, and the differential operator associated with the stability condition generates an adapted basis in which turbulent flow fields may naturally be decomposed. The application and implications of Galerkin truncations in these bases to produce low dimensional dynamical systems models is discussed in the context of thermal convection in a saturated porous layer. © 1997 American Institute of Physics

Publisher: The American Institute of Physics
Year: 1997
DOI identifier: 10.1063/1.54211
OAI identifier:

Suggested articles

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.