Abstract
The first explicit studies of chaos in fluid dynamics belong to the theory of thermal convection. Crude approximations to the fluid equations in the contexts of meteorology (Lorenz, 1963) and astrophysics (Moore & Spiegel, 1966) led to model systems with complicated temporal dynamics. Lorenz gave a prescient discussion of his third-order system of ordinary differential equations that has guided many workers in the theory of chaos. Moore and I were more backward-looking; we tried to interpret the erratic solutions of our model equation, as in Hopf’s perception of turbulence, as a wandering among many unstable periodic solutions. Of course, as fluid dynamics, all this work was unsatisfactory since unacceptable approximations to the fluid equations were used.
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Spiegel, E.A. (1985). Chaos and Coherent Structres in Fluid Flows. In: Dwoyer, D.L., Hussaini, M.Y., Voigt, R.G. (eds) Theoretical Approaches to Turbulence. Applied Mathematical Sciences, vol 58. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1092-4_13
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DOI: https://doi.org/10.1007/978-1-4612-1092-4_13
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