Skip to main content
Log in

Structural Description of Geophysical Random Fields with Non-Gaussian Statistics

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

This article considers an approach to the describing random fields as a set of intense structures with random parameters. Such structures are observed both in optical fields propagating in inhomogeneous media and in fields of hydrodynamic origin, and they are formed because of the focusing of radiation or deformation of flows. Filtration methods and the evolution of such structures are discussed and different modes of structures—modes of periodic and stochastic oscillations—are described.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.

REFERENCES

  1. S. I. Baskakov, Radio Circuits and Signals (Vysshaya shkola, Moscow, 1983) [in Russian].

  2. E. B. Gledzer, F. V. Dolzhanskii, and A. M. Obukhov, Hydrodynamic Type Systems and Their Application (Nauka, Moscow, 1987) [in Russian].

    Google Scholar 

  3. E. B. Gledzer, “Dissipation and intermittency of turbulence in the framework of hydrodynamic approximations,” Izv., Atmos. Ocean. Phys. 41 (6), 667–683 (2005).

    Google Scholar 

  4. V. P. Goncharov and V. I. Pavlov, Hamiltonian Vortex and Wave Dynamics (GEOS, Moscow, 2008) [in Russian].

    Google Scholar 

  5. S. N. Gurbatov, A. I. Saichev, and I. G. Yakushkin, “Nonlinear waves and one-dimensional turbulence in nondispersive media,” Phys.-Usp. 26 (10), 857–876 (1983).

    Google Scholar 

  6. S. D. Danilov, V. A. Dovzhenko, and I. G. Yakushkin, “Transport of a passive scalar and Lagrangian chaos in a Hamiltonian hydrodynamic system,” J. Exp. Theor. Phys. 91 (2), 423–432 (2000).

    Article  Google Scholar 

  7. F. V. Dolzhansky, V. A. Krymov, and D. Yu. Manin, “Stability and vortex structures of quasi-two-dimensional shear flows,” Sov. Phys. Usp. 33 (7), 495–520 (1990).

    Article  Google Scholar 

  8. F. V. Dolzhansky, “Transverse structures of quasi-two-dimensional geophysical and magnetohydrodynamic flows,” Izv., Atmos. Ocean. Phys. 35 (2), 147–156 (1999).

    Google Scholar 

  9. F. V. Dolzhansky and V. M. Ponomarev, “Simplest slow manifolds of barotropic and baroclinic motions of a rotating fluid,” Izv., Atmos. Ocean. Phys. 38 (3), 277–290 (2002).

    Google Scholar 

  10. F. V. Dolzhansky, “On the mechanical prototypes of fundamental hydrodynamic invariants and slow manifolds,” Phys.-Usp. 48 (12), 1205–1234 (2005).

    Article  Google Scholar 

  11. F. V. Dolzhansky, Fundamentals of Geophysical Hydrodynamics (Fizmatlit, Moscow, 2011) [in Russian].

    Google Scholar 

  12. J. M. Zaiman, Models of Disorder (Cambridge University Press, Cambridge, 1979; Nauka, Moscow, 1982) [in Russian].

  13. G. M. Zaslavskii and R. Z. Sagdeev, Introduction to Nonlinear Physics (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  14. G. M. Zaslavskii, R. Z. Sagdeev, D. A. Usikov, and A. A. Chernikov, Weak Chaos and Quasi-Regular Structures (Nauka, Moscow, 1991) [in Russian].

    Google Scholar 

  15. G. M. Zaslavskii, Physics of Chaos in Hamiltonian Systems (Inst. komp’yuternykh issledovanii, Moscow–Izhevsk, 2004) [in Russian].

  16. Ya. B. Zel’dovich, S. A. Molchanov, A. A. Ruzmaikin, and D. D. Sokolov, “Intermittency in random media,” Sov. Phys. Usp. 30 (5), 353–369 (1987).

    Article  Google Scholar 

  17. V. I. Klyatskin and I. G. Yakushkin, “Stochastic transport in random wave fields,” J. Exp. Theor. Phys. 91 (4), 736–747 (2000).

    Article  Google Scholar 

  18. V. I. Klyatskin, Statistical Analysis of Coherent Phenomena in Stochastic Dynamical Systems (URSS, Moscow, 2014) [in Russian].

    Google Scholar 

  19. V. I. Klyatskin, “Stochastic structure formation in random media,” Phys.-Usp. 59 (1), 67–95 (2016).

    Article  Google Scholar 

  20. S. V. Kostrykin, A. A. Khapaev, and I. G. Yakushkin, “Vortex patterns in quasi-two-dimensional flows of a viscous rotating fluid,” J. Exp. Theor. Phys. 111 (2), 344–354 (2011).

    Article  Google Scholar 

  21. Yu. A. Kravtsov and Yu. I. Orlov, Geometric Optics of Inhomogeneous Media (Nauka, Moscow, 1980) [in Russian].

    Google Scholar 

  22. A. Lichtenberg and M. Lieberman, Regular and Chaotic Dynamics (Springer, 1983; Nauka, Moscow, 1984).

  23. E. Lorentz, The Nature and Theory of the General Circulation of the Atmosphere (WMO, 1967; Gidrometeoizdat, Leningrad, 1970).

  24. A. S. Monin and A. M. Yaglom, Statistical Fluid Dynamics (Nauka, Moscow, 1965), Vols. 1–2 [in Russian].

    Google Scholar 

  25. A. M. Obukhov, Turbulence and Atmospheric Dynamics (Gidrometeoizdat, Leningrad, 1988) [in Russian].

    Google Scholar 

  26. V. M. Ponomarev, A. A. Khapaev, and I. G. Yakushkin, “Nonlinear Ekman friction and asymmetry of cyclonic and anticyclonic coherent structures in geophysical flows,” Dokl. Earth Sci. 425 (2), 505–515 (2009).

    Article  Google Scholar 

  27. M. I. Rabinovich and A. B. Ezerskii, Dynamical Theory of Morphogenesis (Yanus-K, Moscow, 1998) [in Russian].

    Google Scholar 

  28. M. I. Rabinovich and D. I. Trubetskov, Introduction to the Theory of Oscillations and Waves (Regulyarnaya i khaoticheskaya dinamika, 2000) [in Russian].

  29. N. N. Romanova and I. G. Yakushkin, “Hamiltonian description of motion in a perfect stratified fluid,” Dokl. Phys. 48 (5), 742–746 (2001).

    Article  Google Scholar 

  30. N. N. Romanova, O. G. Chkhetiani, and I. G. Yakushkin, “Influence of nonlinear interactions on the development of instability in hydrodynamic wave systems,” J. Exp. Theor. Phys. 122 (5), 902–914 (2016).

    Article  Google Scholar 

  31. S. M. Rytov, Yu. A. Kravtsov, and Yu. A. Tatarskii, Introduction to Statistical Radiophysics, Vol. 2: Random Fields (Nauka, Moscow, 1978) [in Russian].

  32. V. I. Tatarskii, Wave Propagation in the Turbulent Atmosphere (Nauka, Moscow, 1967) [in Russian].

    Google Scholar 

  33. I. G. Yakushkin, “Intensity fluctuations of the field of A plane wave behind A random phase screen,” Radiophys. Quantum Electron. 17 (9), 1032–1036 (1974).

    Article  Google Scholar 

  34. I. G. Yakushkin, “Intensity fluctuations during small-angle scattering of wave fields (review),” Radiophys. Quantum Electron. 28 (5), 365–389 (1985).

    Article  Google Scholar 

  35. I. G. Yakushkin, Abstract of Doctoral Dissertation in Physics and Mathematics (Moscow, 1987).

  36. I. G. Yakushkin, “On light flare flickering on the sea surface,” Izv. Akad. Nauk SSSR: Fiz. Atmos. Okeana 26 (10), 25–32 (1990).

    Google Scholar 

  37. I. G. Yakushkin, “Random internal gravity waves in the atmosphere,” Izv., Atmos. Ocean. Phys. 34 (5), 585–591 (1998).

    Google Scholar 

  38. I. G. Yakushkin, “Lagrangian and Hamiltonian description of models for geophysical flows of ideal fluids,” Izv., Atmos. Ocean. Phys. 41 (2), 127–136 (2005).

    Google Scholar 

  39. R. F. Blackwelder, “Coherent structures associated with turbulent transport,” in Transport Phenomena in Turbulent Flows: Theory, Experiment, and Numerical Simulation: Proceedings of the Second International Symposium (Tokyo, 1987), pp. 1–20.

  40. E. Van Groesen, “Deformation of coherent structures,” UK Rep. Prog. Phys. 59, 511–600 (1996).

    Article  Google Scholar 

  41. A. Guha and G. A. Lawrence, “A wave interaction approach to studying non-modal homogeneous and stratified shear instabilities,” J. Fluid Mech. 755, 336–364 (2014).

    Article  Google Scholar 

  42. J. Jimenez, “Coherent structures in wall-bounded turbulence,” J. Fluid Mech. 842, 1–100 (2018).

    Article  Google Scholar 

  43. S. V. Kostrykin, A. A. Khapaev, and I. G. Yakushkin, “The influence of nonlinear bottom friction on the properties of decaying cyclonic and anticyclonic vortex structures in a shallow rotated fluid,” J. Fluid Mech. 753, 217–241 (2014).

    Article  Google Scholar 

  44. Y. A. Kravtsov, “Propagation of electromagnetic waves through turbulent atmosphere,” Rep. Progr. Phys. 55 (1), 92–112 (1992).

    Article  Google Scholar 

  45. A. Z. Loesch, “Resonant interactions between unstable and neutral baroclinic waves: Part I,” J. Atmos. Sci. 31, 1177–1201 (1974).

    Article  Google Scholar 

  46. M. S. Longuet-Higgins, “The statistical geometry of a random surface,” in Hydrodynamic Stability: Proc. 13-th Symp. Appl. Math. Am. Math. Soc. (1962), pp. 105–142.

  47. E. N. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci. 20 (3), 130–148 (1963).

    Article  Google Scholar 

  48. A. Okubo, “Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences,” Deep-Sea Res. 17, 445–454 (1970).

    Google Scholar 

  49. E. N. Pelinovsky, E. G. Shurgalina, A. V. Sergeeva, T. G. Talipova, and R. H. J. Grimshaw, “Two-soliton interaction as an elementary act of soliton turbulence in integrable systems,” Phys. Lett. A 377, 272–275 (2013).

    Article  Google Scholar 

  50. N. N. Romanova and S. A. Annenkov, “Three-wave resonant interactions in unstable media,” J. Fluid Mech. 539, 57–91 (2005).

    Article  Google Scholar 

  51. R. Salmon, “Hamiltonian fluid mechanics,” Ann. Rev. Fluid Mech. 20, 225–256 (1988).

    Article  Google Scholar 

  52. G. K. Vallis, Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large-Scale Circulation (Cambridge University Press, Cambridge, 2017).

    Book  Google Scholar 

  53. I. G. Yakushkin and V. U. Zavorotny, “Statistics evolution of Gaussian wave fields in random media,” Waves Random Media 2, 162–165 (1992).

    Article  Google Scholar 

  54. I. G. Yakushkin, “Strong focusing of plane wave behind a power-law phase screen,” Waves Random Media 6, 281–289 (1996).

    Article  Google Scholar 

Download references

ACKNOWLEDGMENTS

The author is deeply grateful to colleagues for our discussions of the problems raised in the article and for teaching me much. Special thanks go out to A.A. Khapaev as well for constant attention and assistance.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to I. G. Yakushkin.

Ethics declarations

The author declares that he has no conflicts of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yakushkin, I.G. Structural Description of Geophysical Random Fields with Non-Gaussian Statistics. Izv. Atmos. Ocean. Phys. 59, 150–166 (2023). https://doi.org/10.1134/S0001433823020093

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433823020093

Keywords:

Navigation