Strange Attractors in Geophysical Flow Fields
LA JOLLA INST CA DIV OF APPLIED NONLINEAR PROBLEMS
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The techniques of nonlinear dynamics system theory be usefully applied in a physical oceanography context Tentatively, yes, the dynamics of a numerically generated one-dimensional sea surface is shown to take place on a low-dimensional attractor. Further, the dimension of the attractor is fractional noninteger and therefore the trajectory describing the surface evolution is chaotic. The first section reviews the traditional wisdom of the mathematical modeling of waves on the sea surface. In the second section a mini-review of nonlinear dynamics is presented, in which the basic concepts of importance in understanding the influence of nonlinearities on the evolution of a system are discussed in a straightforward way. How these concepts have been applied in geophysical context, including the ocean surface, is discussed in Section 3. In particular it is shown that both climate and weather have chaotic attractors using a technique that allows one to reconstruct the attractor directly from observational data. The properties of the sea surface modeled as a fractal surface are also discussed. In Section 4 some original research is presented in which the attractor reconstruction technique is applied to a numerically generated one-dimensional sea surface having a Phillips spectrum of waves. These calculations find that the water wave attractor has a low-order fractional dimension. This implies that as few as five or six degrees of freedom may be sufficient to describe the dynamics of a surface that required 512 degrees of freedom to numerically generate.
- Physical and Dynamic Oceanography
- Numerical Mathematics
- Fluid Mechanics