There are special circumstances when the equations of fluid mechanics can be asymptotically reduced to third- or higher-order differential equations that admit chaotic solutions. For physically extended systems, similar reductions lead to simplified partial differential equations whose solutions contain coherent structures that interact in complicated and erratic ways. It is suggested here that analogous reductions of the fluid equations are possible even when the fluid is in a turbulent state. From this we conclude that, more than being a metaphor for turbulence, chaos is a basic property of turbulent fluids.
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E. A. Spiegel (1987) studied this question.
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