Summer study program in geophysical fluid dynamics : chaos

Abstract

The explosive growth of dynamieal systems theory in the past two decades stems in large part from the realization that it is applicable to many natural phenomena. Indeed, much o f the theoretical development has been sparked by numerical and laboratory experiments which exhibit ordered sequences of behavior that call for a general framework of interpretation We have been fortunate this summer to have had in residence both pioneers and developers of dynamical systems theory and its applications to fluid mechanics. Several recent texts contain the basic principles that Ed Spiegel used as a springboard for five lectures in which he exposed us to elementary examples of bifurcation and chaos, to symmetry breaking, normal forms and temporal and spatial disorder, as well as to pertinent fluid mechanical and astrophysical phenomena. Yves Pomeau continued the development with an elegant summary of different types of intermittency . Stephan Fauve agree to write up his impressive seminars on phase instability and turbulence as an extension of the lecture series. Many of the remaining seminars introduced new concepts in the theory, some with specific examples, others via mathematical development, and still others through ways of interpreting the data that emerge from calculations and experiments. As an outstanding example of this, Albert Libchaber has demonstrated the fascinating correspondence between the frequencies observed in one of his recent fluid mechanics experiments and results from number theory relating the Fibonacci series to the golden mean.