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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Equilibrium Distributions for Hydrodynamic Flows

Discontinuity, Nonlinearity, and Complexity 4(3) (2016) 243--255 | DOI:10.5890/DNC.2016.09.003

V.I. Klyatskin

A. M. Obukhov Institute of Atmospheric Physics RAS, Moscow, Pyzhevsky per. 3, 119017, Russia

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This paper deals with the problem of stochastic structure formation in random hydrodynamic flows. In particular, starting from an analysis of the steady-state probability density, it considers coherent structures of vortex formation (vortex genesis) in stochastic quasi-geostrophic flows, which are related to rotation and random topography of the bottom.


This work was supported by the RSF 14-27-00134.


  1. [1]  Hopf, E. (1952), Statistical hydromechanics and functional calculus, J. Rat. Mech. Anal., 1, 87-123.
  2. [2]  Hopf, E. (1957), On the application of functional calculus to the statistical theory of turbulence, in: Proceedings of Symposia in Applied Mathematics , 7, 41-50, Am. Math. Society.
  3. [3]  Hopf, E. (1962), Remarks on the functional-analytic approach to turbulence, in: Proceedings of Symposia in Applied Mathematics, 13, 157-163, Am. Math. Society.
  4. [4]  Hopf, E. and Titt, E.W. (1953), On certain special solution of the equation of statistical hydrodynamics, J. Rat. Mech. Anal., 2, 587.
  5. [5]  Landau, L.D. and Lifshitz, E.M. (1987), Fluid Mechanics, Second edition, Pergamon Press, London.
  6. [6]  Klyatskin, V.I. (1969), On Statistical theory of two-dimensional turbulence, Journal of Applied Mathematics and Mechanics, 33(5), 864-866.
  7. [7]  Kraichnan, R.H. (1967), Inertial waves in two-dimensional turbulence, Physics of Fluids, 10, 1417-1423.
  8. [8]  Kraichnan, R.H. (1975), Statistical dynamics of two-dimensional flows, Journal of Fluid Mechanics, 67, 155-175.
  9. [9]  Kraichnan, R.H. and Montgomery, D. (1980), Two-dimensional turbulence, Reports on Progress in Physics, 43, 547- 619.
  10. [10]  Miller, J., Weichman P. and Cross, M. (1992), Statistical mechanics, Euler*s equation and Jupiter*s red spot, Physical Review, A45(4), 2328-2359.
  11. [11]  Fofonoff, N. (1954), Steady flow in a frictionless homogeneous ocean, Journal Of Marine Research, 13, 254-262.
  12. [12]  Pedlosky, J. (1982), Geophysical Fluid Dynamics, Springer-Verlag, New York.
  13. [13]  Klyatskin, V.I. (1995), Equilibrium states for quasigeostrophic flows with random topography, Izvestiya, Atmospheric and Oceanic Physics, 31(6), 717-722.
  14. [14]  Klyatskin, V.I. and Gurarie, D. (1996), Random topography in geophysical models, in: Stochastic Models in Geosystems, eds. Molchanov, S.A. and Woyczynski, W.A. IMA Volumes in Math. and its Appl. 85, 149-170. N.Y. Springer- Verlag.
  15. [15]  Klyatskin, V.I. and Gurarie D. (1996), Equilibrium states for quasigeostrophic flows with random topography, Physica D, 98, 466-480.
  16. [16]  Hopfinger, E.J. and Browand, F.K. (1982), Vortex solitary waves in rotating, turbulent flow, Nature, 295(5848), 393- 394.
  17. [17]  Hopfinger, E.J. (1989), Turbulence and vortices in rotating fluids, in: Theoretical and Applied Mechanics, 117-138. Germain, P., Piau, M. and Caillerie, D. (Editors), IUTAM, Elsevier Science Publishers B.V. (North-Holland).
  18. [18]  Boubnov, B.M. and Golitsyn, G.S. (1986), Experimental study of convective structures in rotating fluids, Journal of Fluid Mechanics, 167(6), 503-531.
  19. [19]  Boubnov, B.M. and Golitsyn, G.S. (1995), Convection in Rotating Fluids, Ser. Fluid Mechanics and its Applications, Vol. 29, Dordrecht, Boston, London: Kluver Academic Publishers.
  20. [20]  Pavlov, V., Buisine, D. and Goncharov, V. (2001), Formation of vortex clusters on a sphere, Nonlinear Processes In Geophysics, 8, 9-19.
  21. [21]  Karimova, S.S., Lavrova, O.Yu. and Solov*ev, D.M. (2012), Observation of Eddy Structures in the Baltic Sea with the use of Radiolocation and Radiometric Sattelite Data, Izvestiya, Atmos. and Oceanic Phys., 49(9), 1006-1013.
  22. [22]  Karimova, S. (2012), Spiral eddis in the Baltic, Black and Caspian seas as seen by satellite radar data, Advances in Space Research, 50, 1107-1124.