Turbulence in Fluid Flows

1. Front Matter

   Pages i-xv

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2. Application of an Approximate R-N-G Theory, to a Model for Turbulent Transport, with Exact Renormalization

   • Marco Avellaneda, Andrew J. Majda

   Pages 1-31

3. Weak and Strong Turbulence in the Complex Ginzburg Landau Equation

   • J. D. Gibbon

   Pages 33-48

4. Symmetries, Heteroclinic Cycles and Intermittency in Fluid Flow

   • Philip Holmes

   Pages 49-58

5. Finite-Dimensional Description of Doubly Diffusive Convection

   • E. Knobloch, M. R. E. Proctor, N. O. Weiss

   Pages 59-72

6. Dynamical Stochastic Modeling of Turbulence

   • Robert H. Kraichnan

   Pages 73-86

7. On a New Type of Turbulence for Incompressible Magnetohydrodynamics

   • V. P. Maslov

   Pages 87-100

8. Loss of Stability of the Globally Unique Steady-State Equilibrium and the Bifurcation of Closed Orbits in a Class of Navier-Stokes Type Dynamical Systems

   • Gheorghe Minea

   Pages 101-122

9. Turbulent Bursts, Inertial Sets and Symmetry-Breaking Homoclinic Cycles in Periodic Navier-Stokes Flows

   • Basil Nicolaenko, Zhen-Su She

   Pages 123-136

10. Navier-Stokes Equations in Thin 3D Domains III: Existence of a Global Attractor

    • Geneviève Raugel, George R. Sell

    Pages 137-163

11. An Optimality Condition for Approximate Inertial Manifolds

    • George R. Sell

    Pages 165-186

12. Some Recent Results on Infinite Dimensional Dynamical Systems

    • Roger Temam

    Pages 187-197

The articles in this volume are based on recent research on the phenomenon of turbulence in fluid flows collected by the Institute for Mathematics and its Applications. This volume looks into the dynamical properties of the solutions of the Navier-Stokes equations, the equations of motion of incompressible, viscous fluid flows, in order to better understand this phenomenon. Although it is a basic issue of science, it has implications over a wide spectrum of modern technological applications. The articles offer a variety of approaches to the Navier-Stokes problems and related issues. This book should be of interest to both applied mathematicians and engineers.

• Fluid Flows
• Navier-Stokes equation
• Turbulence
• convection
• differential equation
• magnetohydrodynamics

• School of Mathematics, University of Minnesota, Minneapolis, USA

  George R. Sell

• Department of Mathematics, Indiana University, Bloomington, USA

  Ciprian Foias

• Laboratoire d’Analyse Numérique, Université Paris-Sud, Orsay, France

  Roger Temam

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