Leonardo Da Vinci, Andrei Kolmogorov And Giorgio Parisi. The Energy Decay Of Turbulence From Leonardo To Multifractal Theory

2023-01-30 Prof. Uriel Frisch, Observatoire de la Côte d’Azur, Nice, France

ABSTRACT :

Leonardo da Vinci had a strong interest in hydrodynamics. Around 1505 he got interested in “turbulence” (he was the first to use this name). Examining the “turbulences” (eddies) in the river Arno of Florence, he found that the amplitude of the turbulence was decreasing very slowly in time, until it would come to rest (within the surrounding river). In spite of Leonardo’s strong interest in mathematics, at that time, it consisted basically of geometry and simple polynomial equations. There were no tools available to describe the very slow temporal relaxation of turbulence. This topic would remain dormant for about 430 years, until in 1938 Karman, triggered by Taylor, established that the mean energy of the turbulence should decrease very slowly, indeed like an inverse power of the time elapsed. Three years later, Kolmogorov himself found another inverse power (10/7) of the time elapsed. This, likewise was wrong, because he was assuming a certain invariance property (Loitsiansky , proved later wrong by Proudman and Reid). The main change in the last few decades is that fully developed turbulence is definitely not self-similar, not only is it fractal, but it can have infinitely many fractal scalings (multifractality), as proposed by Parisi and Frisch in the eighties. Furthermore, multifractality can manifest itself either at small scales or at large scales. The latter might change the law of energy decay. Not enough is understood for the 3D Euler equations, but large-scale multifractality for the Burgers is an interesting possibility, which is being explored by Frisch, Khanin, Pandit and Roy. A brief exploration of what happens to the energy decay-law will be presented.

Event Name

Seminars

Place

Online

Start Time

14:30

End Time

15:30

External Link

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