Seminar by Prof. Uriel Frisch on 30th Jan at 2:30 pm
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Urna Basu
Jan 29, 2023, 7:05:40 AM1/29/23
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Dear All,
You are invited to join the next talk in the Statistical Mechanics Seminar
Series organized by S.N. Bose Center. Please find the details below.
Speaker: Prof. Uriel Frisch
Affiliation: Observatoire de la Côte d'Azur, Nice, France
Date & Time: 30.01.2023, 02:30 PM (IST)
Webinar Link: https://meet.google.com/agb-ppqn-mef
Title: Leonardo da Vinci, Andrei Kolmogorov and Giorgio Parisi.
The energy decay of turbulence from Leonardo to multifractal theory
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.
Sincerely,
Sakuntala Chatterjee, Suman Chakraborty, Punyabrata Pradhan and Urna Basu
You are invited to join the next talk in the Statistical Mechanics Seminar
Series organized by S.N. Bose Center. Please find the details below.
Speaker: Prof. Uriel Frisch
Affiliation: Observatoire de la Côte d'Azur, Nice, France
Date & Time: 30.01.2023, 02:30 PM (IST)
Webinar Link: https://meet.google.com/agb-ppqn-mef
Title: Leonardo da Vinci, Andrei Kolmogorov and Giorgio Parisi.
The energy decay of turbulence from Leonardo to multifractal theory
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.
Sincerely,
Sakuntala Chatterjee, Suman Chakraborty, Punyabrata Pradhan and Urna Basu
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