Convection, stability, and low dimensional dynamics

Journal Article · Thu May 01 04:00:00 EDT 1997 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.54211· OSTI ID:586270

Doering, C R ^[1]

---

1. Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109 (United States)

Recent developments concerning the connection between notions of hydrodynamic stability{emdash}usually associated with stationary laminar flows{emdash}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 {open_quotes}marginal stability{close_quotes} 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. {copyright} {ital 1997 American Institute of Physics.}

• Sponsoring Organization: USDOE
• OSTI ID: 586270
• Report Number(s): CONF-970728--
• Journal Information: AIP Conference Proceedings, Journal Name: AIP Conference Proceedings Journal Issue: 1 Vol. 411; ISSN APCPCS; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
CONVECTION
HYDRODYNAMICS
NONLINEAR PROBLEMS
POROUS MATERIALS
STABILITY
TURBULENCE