Chaos and Turbulence
Abstract
The main research effort was an attempt to find low order systems possessing chaotic behavior which could successfully model turbulent flow. The reason for searching for low order systems is the strongly suggestive evidence that 'chaos' disappears in systems with a large number of degrees of freedom. Recent work on symplectic integration of Hamiltonian systems indicates that for Hamiltonian systems chaos may be no more than numerical error growing exponentially, and is absent when the numerical scheme conserves the Poincare invariants and the symplectic structure. A great deal was learned about vortical solutions of the Navier-Stokes equations and new solutions of a weakly nonlinear approximation were found, which suggest the existence of Navier-Stokes solutions which will describe a vortical description of the laminar turbulent interface. An interesting application of dynamical system theory to a problem of kinematic mixing showed that the use of these ideas could reduce the dimension of the system in order to make computations feasible, and predict the qualitative development of the distribution of mixed tracer in an unsteady flow. (edc)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 31, 1989
- Accession Number
- ADA215310
Entities
Organizations
- California Institute of Technology