Clouds and Turbulence Theory: Peculiar Self-Similarity, 4/3 Fractal Exponent and Invariants
- Authors: Golitsyn G.S.1, Chkhetiani O.G.1, Vazaeva N.V.1,2
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Affiliations:
- Obukhov Institute of Atmospheric Physics Russian Academy of Science
- Bauman Moscow State Technical University
- Issue: Vol 59, No 2 (2023)
- Pages: 242-244
- Section: Articles
- URL: https://journals.rcsi.science/0002-3515/article/view/136928
- DOI: https://doi.org/10.31857/S0002351523020025
- EDN: https://elibrary.ru/HNMBQJ
- ID: 136928
Cite item
Abstract
In 1982 Lovejoy has published an illustration to Mandelbrot proposal how to characterize the area-perimeter ratio of complicated planar forms and it was found that exponent \(\beta \) for the satellite- and radar-determined cloud and rain areas of such a fractal is 1.35 close to 4/3. Later on it was notified that the same exponent was found also for noctilucent clouds. Such a value might be related to classic turbulence theory of 1941. This text demonstrates this relation using two basic papers by Kolmogorov and Obukhov. The role of prefractal multipliers is revealed, they form a couple of the peculiar invariants for cloud fields and a non-dimensional self-similarity numbers for these fields of sizes \(1 - {{10}^{6}}\,\,{\text{k}}{{{\text{m}}}^{2}}.\) The peculiarity is in their dimensional dependence and in the presence of few invariants, not usual invariants in cloud forms. Further research on random walk of a fluid particle in the 6D phase-space may lead to new discoveries.
Keywords
About the authors
G. S. Golitsyn
Obukhov Institute of Atmospheric Physics Russian Academy of Science
Author for correspondence.
Email: gsg@ifaran.ru
Russia, 119017, Moscow, Pyzhovskiy per., 3
O. G. Chkhetiani
Obukhov Institute of Atmospheric Physics Russian Academy of Science
Author for correspondence.
Email: ochkheti@gmail.com
Russia, 119017, Moscow, Pyzhovskiy per., 3
N. V. Vazaeva
Obukhov Institute of Atmospheric Physics Russian Academy of Science; Bauman Moscow State Technical University
Author for correspondence.
Email: vazaevanv@ifaran.ru
Russia, 119017, Moscow, Pyzhovskiy per., 3; Russia, 105005, Moscow, 2-ya Baumanskaya str., 5, bld. 1
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