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Abstract: Chaotic motion in time of a number of macroscopic systems has been analyzed,in the framework of scale relativity, as motion in a fractal space withtopological dimension 3 and geodesics with fractal dimension 2. The motionequation is then Schr\-odinger-like and its interpretation in fluid mechanicsgives the well-known Euler and Navier-Stokes equations. We generalize here thisformalism to the study of a system exhibiting a chaotic behavior both in spaceand time. We are thus lead to consider macroscopic fluid properties as issuingfrom the geodesic features of a fractal `space-time- with topological dimension4 and geodesics with fractal dimension 2. This allows us to obtain both amotion equation for the fluid velocity field, which exhibits then threecomponents while only one is necessary for the description of an ordinaryfluid, and a relation between their three curls. The physical properties ofthis solution suggest it could represent some three-dimensional chaoticbehavior for a classical fluid, tentatively turbulent if particular conditionsare fulfilled. Different ways of testing experimentally these assumptions areproposed.



Autor: Marie-Noëlle Célérier LUTH, Observatoire de Paris

Fuente: https://arxiv.org/







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