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• W1639873732 abstract "In the past, the unpredictability of turbulent flows has been understood in the framework of dynamical system theory, and the words or weak turbulence are commonly used to describe flows with temporal erratic behaviors but simple spatial structures. Such situations exist in laboratory experiments, where the spatial degrees of freedom can be quenched by the boundary conditions or by external fields. The main result relative to these highly constrained flows is that the phenomena underlying chaos are finite dimensional although the state space for a fluid is infinite dimensional. This was first conjectured by Ruelle and Takens-^in 1971 as a challenge to Landau's view of a chaotic state, described as a quasiperiodic one with many independent frequencies. In 1975, the experimental results of Gollub and Swinney^ corroborated the idea of Ruelle and Takens-^-. They observed in a Couette-flow experiment that a few nonlinearly coupled modes are enough to produce a chaotic behavior. It should be noted that systems of nonlinear ordinary differential equations that display chaotic regimes, have been known since the work of Chirikov on Hamiltonian systems^ and also since the numerical computations of Lorenz on a three-mode truncation of the equations governing finite-amplitude convection in a fluid layer heated from below^. The Lorenz system motivated a variety of numerical studies on systems of differential equations and on finite-difference equations^ that exhibited various possible routes to chaos. The best theoretically and experimentally documented one is the period-doubling scenario:'** the system achieves chaotic temporal behavior through the production of successive half-harmonics. First observed in a convection experiment in liquid helium,9 it was confirmed with other fluids, water, - and mercury,H for" @default.
• W1639873732 created "2016-06-24" @default.
• W1639873732 creator A5040603744 @default.
• W1639873732 date "1988-01-01" @default.
• W1639873732 modified "2023-09-27" @default.
• W1639873732 title "Competing Instabilities in Rayleigh-B£nard Convection" @default.
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