Studies in Global, Bifurcation and Symmetry

Abstract

Models of Turbulent Boundary Layers used the proper orthogonal decomposition theorem to provide optimal bases for finite dimensional subspaces so that relatively low dimensional projections of the Navier-Stokes equations can be calculated. These dynamical systems retain key features of the turbulence production mechanisms. The inherit symmetries from physical space which lead to the existence of structurally stable heteroclinic cycles, in turn creating intermittent dynamics remarkably similar to the bursting phenomenon observed in experiments. Ours are perhaps the first rationally derived low (-10-50) dimensional models for turbulence in open flows and they offer promise of improved understanding of basic mechanisms and design of drag control strategies. Unlike other groups using Karhunen-Loeve methods, we have carried out rather complete analyses of the projected ODE's. This work resulted in papers and also led to the mathematical questions.

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Document Details

Document Type
Technical Report
Publication Date
May 31, 1991
Accession Number
ADA243862

Entities

People

  • Phillip Holmes

Organizations

  • Cornell University College of Engineering

Tags

Communities of Interest

  • Autonomy
  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Boundary Layer
  • Computational Complexity
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Dynamics
  • Equations
  • Fluid Mechanics
  • Mathematics
  • Mechanics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Surface Waves
  • Symmetry
  • Turbulence
  • Turbulent Boundary Layer

Readers

  • Calculus or Mathematical Analysis
  • Fluid Mechanics and Fluid Dynamics.
  • Systems Analysis and Design

Technology Areas

  • Space