Turbulence in Fluid Flows: A Dynamical Systems Approach

✍ Scribed by Marco Avellaneda, Andrew J. Majda (auth.), George R. Sell, Ciprian Foias, Roger Temam (eds.)

• Publisher: Springer-Verlag New York
• Year: 1993
• Tongue: English
• Leaves: 207
• Series: The IMA Volumes in Mathematics and its Applications 55
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xv
Application of an Approximate R-N-G Theory, to a Model for Turbulent Transport, with Exact Renormalization....Pages 1-31
Weak and Strong Turbulence in the Complex Ginzburg Landau Equation....Pages 33-48
Symmetries, Heteroclinic Cycles and Intermittency in Fluid Flow....Pages 49-58
Finite-Dimensional Description of Doubly Diffusive Convection....Pages 59-72
Dynamical Stochastic Modeling of Turbulence....Pages 73-86
On a New Type of Turbulence for Incompressible Magnetohydrodynamics....Pages 87-100
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....Pages 101-122
Turbulent Bursts, Inertial Sets and Symmetry-Breaking Homoclinic Cycles in Periodic Navier-Stokes Flows....Pages 123-136
Navier-Stokes Equations in Thin 3D Domains III: Existence of a Global Attractor....Pages 137-163
An Optimality Condition for Approximate Inertial Manifolds....Pages 165-186
Some Recent Results on Infinite Dimensional Dynamical Systems....Pages 187-197

✦ Subjects

Analysis