Causes and effects of chaos
Abstract
Chaos was first discovered in turbulent fluid flow, considered the unsolved problem in classical physics. Fluid flow turns from smooth (laminar) to turbulent as its velocity increases. The classic explanation for this was that new frequencies appeared, one at a time, in the velocity and density profiles. In the early 1960's, a meteorology professor at MIT named Edward Lorenz simulated the actions of an air mass between warm ground and cool clouds, modeled by a simplified version of the NavierStokes equations for fluid flow. Mathematically, the definition of chaotic behavior requires: sensitive dependence upon initial conditions topological transitivity and dense periodic points in the Poincare section of the system's state space. Sensitive dependence is illustrated by Smale's horseshoe, the nonlinear transformation.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 December 1990
 Bibcode:
 1990STIN...9213405B
 Keywords:

 Air Masses;
 Atmospheric Models;
 Atmospheric Physics;
 Chaos;
 Clouds (Meteorology);
 NavierStokes Equation;
 Transformations (Mathematics);
 Turbulent Flow;
 Classical Mechanics;
 Fluid Flow;
 Meteorology;
 Nonlinear Systems;
 Turbulence;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer