On the Theory of Turbulent Dynamics.
Abstract
Acceptance of the discovery of amplification of intrinsic fluctuations by chaotic dynamics has been slow. They have been able to identify several of the mental blocks experienced by others and have successfully clarified their position for some of these people. But it has been a slow process. The principal problem has been that some earlier researchers saw amplification of intrinsic fluctuations in their own work but failed to recognize its significance. These include Robert Graham and B. Huberman. The two conceptual insights they have missed are: (1) such amplification invalidates the contraction of the description from the mesoscopic level to the macroscopic level; and (2) the centrality of the Jacobi matrix in the theory since it connects the magnitude (and sign) of the largest Liapunov exponent with the growth of the fluctuations. The first oversight by others follows from their failure to embed the phenomenon in the context of levels of description. Rather, in their work, they have simply added fluctuations to macroscopic equations and investigated what happens. The second oversight results from not suspecting a connection in the first place.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 30, 1992
- Accession Number
- ADA258695
Entities
People
- Ronald F. Fox
Organizations
- Georgia Tech