Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school

Gledzer E B; Golitsyn G S

doi:10.2205/2019ES000651

KAULA'S RULE - A CONSEQUENCE OF PROBABILITY LAWS BY A. N. KOLMOGOROV AND HIS SCHOOL Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school

АА Аа

Опубликовано в Russian Journal of Earth Sciences · Рубрика: ОРИГИНАЛЬНЫЕ СТАТЬИ

DOI: https://doi.org/10.2205/2019ES000651

Получено: 25.12.2019 Одобрено: 25.12.2019 Опубликовано: 25.12.2019 Язык публикаций: ENG

Авторы

Gledzer E B

Golitsyn G S

Gledzer E B

A. M. Obukhov Institute of Atmospheric Physics RAS

Golitsyn G S

A. M. Obukhov Institute of Atmospheric Physics RAS

АННОТАЦИЯ

The paper analyzes a possible cause for the universal behavior of the covariating fluctuations of planet gravity. The consideration based on the idea that the topography fluctuations are governed by a random Markov process leads to universal dependence k−2" role="presentation" style="position: relative;">k-2k-2k^{-2} with k" role="presentation" style="position: relative;">kkk being the amplitudes of the j" role="presentation" style="position: relative;">jjj-th spherical harmonic of the terrain profile. This law known as the Kaula's rule is then derived from the solution of the Fokker - Plank equation for the fluctuations of the terrain profile as the function of the horizontal coordinate. The respective diffusivities for Earth and Venus are retrieved from the existing data.

КЛЮЧЕВЫЕ СЛОВА

Kaula's rule, Thumb rule, planet gravity, Fokker-Planck equation

Финансирование

We thank A. A. Lushnikov for carefully reading the manuscript and indicating some errors in the formulas. This work has been particularly supported by the RAS Presidium Program No. 7 "The development of non-linear methods in theoretical and mathematical physics". The authors are very thankful to Dr. O. G. Chkhetiany for discussion of the results and his continuous help during the long work.

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1. Barenblatt, G. I. (1996) , Scaling, Similarity and Intermediate Asymptotics, 386 pp., Cambridge Univ. Press, Cambridge, UK, https://doi.org/10.1017/CBO9781107050242. EDN: https://elibrary.ru/YCVFBU

2. Barenblatt, G. I. (2003) , Scaling, 171 pp., Cambridge Univ. Press, Cambridge, UK, https://doi.org/10.1017/CBO9780511814921.

3. Bridgman, P. W. (1932) , Dimensional Analysis, 113 pp., Yale Univ. Press, London, UK.

4. Gledzer, E. B., G. S. Golitsyn (2010) , Scaling and finite ensembles of particles with the energy influx, Doklady RAS, 433, no. 4, p. 466-470.

5. Golitsyn, G. S. (2001) , The place of the Gutenberg-Richter law among other statistical laws of nature, Comput. Seismology, 77, p. 160-192.

6. Golitsyn, G. S. (2003) , Statistical description of the planetary surface relief and its evolution, Proc. RAS. Physics of the Earth, no. 7, p. 3-8.

7. Golitsyn, G. S. (2018) , Laws of random walks by A. N. Kolmogorov 1934, Soviet Meteorol. Hydrol, no. 3, p. 5-15, https://doi.org/10.3103/S1068373918030019. EDN: https://elibrary.ru/YTHHPT

8. Golitsyn, G. S. (2018) , Random Walk Laws by A. N. Kolmogorov as the bases for understanding most phenomena of the nature, Izv. RAS Atmos. and Ocean. Phys., 54, p. 223-228.

9. Kaula, W. M. (1966) , Theory of Satellite Geodesy, 143 pp., Bleinsdell, Waltham. Ma.

10. Kolmogorov, A. N. (1934) , Zufallige Bewegungen, Ann. Math. , 35, p. 166-117, https://doi.org/10.2307/1968123.

11. Konopliv, A. S., et al. (2014) , The Vesta gravity field, Icarus, 240, p. 103-117, https://doi.org/10.1016/j.icarus.2013.09.005. EDN: https://elibrary.ru/WQZRMH

12. Lindborg, E. (2008) , Stratified turbulence: a possible interpretation of some geophysical turbulence measurements, J. Atmos. Sci., 65, p. 2416-2424, https://doi.org/10.1175/2007JAS2455.1.

13. McMahon, J. W., et al. (2016) , Understanding the Kaula's rule for small bodies, Proc. 47th Lunar and Planetary Sci. Conference, AGU, Washington, DC (https://www.hou.usra.edu/meetings/lpsc2016/pdf 2129.pdf).

14. Monin, A. S., A. M. Yaglom (1975) , The Statistical Hydromechanics, MIT Press, Cambridge (Russ. ed. 1967).

15. Obukhov, A. M. (1941) , On the energy distribution in the spectrum of turbulent flow, Proc. (Doklady) USSR Ac. Sci., 32, no. 1, p. 22-24.

16. Obukhov, A. M. (1959) , Description of turbulence in terms of Lagrangian variables, Adv. Geophys., 6, p. 113-115, https://doi.org/10.1016/S0065-2687(08)60098-9. EDN: https://elibrary.ru/ZYPVVN

17. Rexer, M., C. Hirt (2015) , Ultra-high spherical harmonics analysis and application to planetary topography of Earth, Mars and Moon, Surv. Geophys., 36, no. 6, p. 803-830, https://doi.org/10.1007/s10712-015-9345-z. EDN: https://elibrary.ru/VZHESZ

18. Richardson, L. F. (1926) , Atmospheric diffusion shown on a distance-neighbour graph, Proc. Roy. Soc., A110, no. 756, p. 709-737, https://doi.org/10.1098/rspa.1926.0043.

19. Richardson, L. F. (1929) , A search for the law of atmospheric diffusion, Beitr. Phys. für Atmosphäre, 15, no. 1, p. 24-29.

20. Turcotte, D. L. (1997) , Chaos and Fractals in Geology and Geophysics, 416 pp., Cambridge University Press, New York, https://doi.org/10.1017/CBO9781139174695.

21. Yaglom, A. M. (1955) , Correlation theory for processes with stochastic stationary increments of the n-th order, Math. Collection, 37, no. 1, p. 259-288 (in Russian).

22. Yaglom, A. M. (1986) , Correlation Theory of Stationary and Related Random Functions, 526 pp., Springer Verlag, Berlin.

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ГОСТ

, Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school // Russian Journal of Earth Sciences. 2019. №. 6. С. -. DOI: https://doi.org/10.2205/2019ES000651. (дата обращения: 08.09.2026).

MLA

Gledzer E B, . "Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school." Russian Journal of Earth Sciences 19.6 (2019): -. DOI: https://doi.org/10.2205/2019ES000651.

APA

, (2019). Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school. Russian Journal of Earth Sciences, 19(6), -. https://doi.org/10.2205/2019ES000651

Chicago

Gledzer E B, . "Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school." Russian Journal of Earth Sciences 19, no. 6 (2019): -. https://doi.org/10.2205/2019ES000651.

WIKI

{{cite journal | author = , | title = Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school | journal = Russian Journal of Earth Sciences | year = 2019 | volume = 19 | issue = 6 | pages = - | doi = 10.2205/2019ES000651 }}

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KAULA'S RULE - A CONSEQUENCE OF PROBABILITY LAWS BY A. N. KOLMOGOROV AND HIS SCHOOL Kaula's rule - a consequence of probability laws by A. N. Kolmogorov and his school

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