On the nature of turbulence

  title={On the nature of turbulence},
  author={David Ruelle and Floris Takens},
  journal={Communications in Mathematical Physics},
  • D. Ruelle, F. Takens
  • Published 1 September 1971
  • Physics, Engineering
  • Communications in Mathematical Physics
A mechanism for the generation of turbulence and related phenomena in dissipative systems is proposed. 

Figures from this paper

Roads to turbulence in dissipative dynamical systems
Three scenarios leading to turbulence in theory and experiment are outlined. The respective mathematical theories are explained and compared.
A turbulence model for the solution of two dimensional internal flows by the finite element method
Presents a method of implementing and validating a turbulence model for incompressible and internal flows.
The Turbulent Fluid as a Dynamical System
This paper reviews the applications of the theory of differentiable dynamical systems to the understanding of chaos and turbulence in hydrodynamics. It is argued that this point of view will remain
Predictability, Stability and Chaos in Dynamical Systems
Progress in the theory of stability is presented in the particular example of the Lagrangian motions of the three-body problem and is then generalized.
Strange attractors as a mathematical explanation of turbulence
We discuss a mechanism for the generation of turbulence in viscous fluids. According to this mechanism, first proposed by D. Ruelle and F. Takens [9], the solutions of the equations of motion
Nonequilibrium and Fluctuation Relation
A review on the fluctuation relation, fluctuation theorem and related topics.


Foundations of mechanics
Introduction Foreward by Tudor Ratiu and Richard Cushman Preliminaries Differential Theory Calculus on Manifolds Analytical Dynamics Hamiltonian and Lagrangian Systems Hamiltonian Systems with
Existence and nonuniqueness of rectangular solutions of the Bénard problem
The stable, center-stable, center, center-unstable, unstable manifolds
Differentiate dynamical systems
  • Bull. Am. Math. Soc
  • 1967
Abzweigung einer periodischen Losung von einer stationaien Lδsung eines Differentialsystems
  • Ber. Math.-Phys. Kl. Sachs. Akad. Wiss. Leipzig 94, 1—22
  • 1942
One-dimensional non-wandering sets
A bifurcation theory for nonlinear elliptic partial differential equations and related systems. In: Bifurcation theory and nonlinear eigenvalue problems
  • 1969
Fonctions stationnaires. Functions de correlation. Application a la representation spatio-temporelle de la turbulence
  • Ann. ίnst. Henri Poincare. Section B
  • 1969