Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model
@article{Yorke1979MetastableCT,
title={Metastable chaos: The transition to sustained chaotic behavior in the Lorenz model},
author={James A. Yorke and Ellen D. Yorke},
journal={Journal of Statistical Physics},
year={1979},
volume={21},
pages={263-277}
}The system of equations introduced by Lorenz to model turbulent convective flow is studied here for Rayleigh numbersr somewhat smaller than the critical value required for sustained chaotic behavior. In this regime the system is found to exhibit transient chaotic behavior. Some statistical properties of this transient chaos are examined numerically. A mean decay time from chaos to steady flow is found and its dependence uponr is studied both numerically and (very close to the criticalr…
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36 References
Preturbulence: A regime observed in a fluid flow model of Lorenz
- Physics
- 1979
This paper studies a forced, dissipative system of three ordinary differential equations. The behavior of this system, first studied by Lorenz, has been interpreted as providing a mathematical…
THE ONSET OF CHAOS IN A FLUID FLOW MODEL OF LORENZ *
- Physics
- 1979
There have been many attempts in the scientific literature to provide a mathematical explanation o f the nature of turbulence in fluids, We take the most common approach, arguing that turbulence is a…
Statistical dynamics of the Lorenz model
- Physics
- 1976
The dynamics of the Lorenz model in the “turbulent” regime (r>rT is investigated by applying methods for treating many-body systems. Symmetry properties are used to derive relations between…
Deterministic nonperiodic flow
- Mathematics
- 1963
Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with…
Stability characteristics of a single-phase free convection loop
- PhysicsJournal of Fluid Mechanics
- 1975
Stability characteristics of a single-phase free convection loop are presented. In the experiments, water was placed inside a toroidal glass loop oriented in a vertical plane. The lower half of the…
On the oscillatory instability of a differentially heated fluid loop
- PhysicsJournal of Fluid Mechanics
- 1967
A theoretical discussion is given of the motion of a fluid contained in a tube forming a closed loop that is heated from below and cooled from above. The fluid is assumed to have uniform temperature…
Period Three Implies Chaos
- Mathematics
- 1975
The way phenomena or processes evolve or change in time is often described by differential equations or difference equations. One of the simplest mathematical situations occurs when the phenomenon…
A moment equation description of magnetic reversals in the earth.
- GeologyProceedings of the National Academy of Sciences of the United States of America
- 1976
Low order moments of the alpha dynamo equations in a geophysical regime are related to the dependent variables in a reversing disk dynamo. The link suggests that nonperiodic reversal is an intrinsic…
Transition in circular Couette flow
- PhysicsJournal of Fluid Mechanics
- 1965
Two distinct kinds of transition have been identified in Couette flow between concentric rotating cylinders. The first, which will be called transition by spectral evolution, is characteristic of the…