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Non-homogeneous/Non-local Two-Dimensional Dynamics

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Vortex Structure and Dynamics

Part of the book series: Lecture Notes in Physics ((LNP,volume 555))

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Abstract

In this short review we examine two interesting aspects of the two-dimensional dynamics. On the one hand, we document the non-homogeneous/non-local description of the two-dimensional flows. On the other hand, we discuss the anomalous energy transfer properties of the non-linear term of the 2D Navier-Stokes equations induced by the nonlocal dynamics.

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References

  1. Kraichnan, R., 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417.

    Google Scholar 

  2. Lesieur, M. 1990. Turbulence in Fluids. Second revised edition. Kluwer Academic Publishers.

    Google Scholar 

  3. McWillians, J.C., 1984. Fluid Mech. 146, 21–43.

    Google Scholar 

  4. Borue, V., 1994. Phys.Rev. Lett. 72, 1475

    Google Scholar 

  5. Smith, L.,M. & Yakhot, V., 1994 Finite-size effect in forced two-dimensional turbulence. J. Fluid Mech. 274, 115–138.

    Google Scholar 

  6. Charney, J. (1971). Geostrophic turbulence, J. Atmos. Sci. 28, 1071–1095.

    Article  Google Scholar 

  7. Rhines, P. B., 1979. Ann. Rev. Fluid Mech. 11, 401–411.

    Google Scholar 

  8. Nastrom, G.D., Gage, K.S. & Jasperson, W.H. 1984 Kinetic energy spectrum of large and mesoscale atmospheric process. Nature 310, 5 July, 36–38.

    Google Scholar 

  9. Okubo, A. 1970 Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergence. Deep-Sea Res. 17, 445–454.

    Google Scholar 

  10. Weiss, J. 1991 The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D 48, 273–294.

    Google Scholar 

  11. Brachet, M., Meneguzzi, M., Politano, H. & Sulem, P. 1988 The dynamics of freely decaying two-dimensional turbulence. J. Fluid Mech. 194, 333–349

    Google Scholar 

  12. Ohkitani, K. (1991) Wave number space dynamics of enstrophy cascade in a forced two-dimensional turbulence. Phys. Fluids A 3, 1598–1611.

    Article  MATH  ADS  Google Scholar 

  13. Elhmaidi, D., Provenzale, A. & Babiano, A. 1993 Elementary topology of twodimensional turbulence from a Lagrangian viewpoint and single-particle dispersion. J. Fluid Mech. 257, 533–558.

    Google Scholar 

  14. Basdevant, C. & Philipovich, T. (1994) On the validity of the ”Weiss criterion“ in two-dimensional turbulence, Physica D 73, 17–30.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Hua, B.L. & Klein P. 1998 An exact criterion for the stirring properties of nearly two-dimensional turbulence. Physica D 113, 98–110.

    Google Scholar 

  16. Andreotti, B., Douady, S. & Couder, Y. 1997. About the interaction between vorticity and stretching. In Turbulent modeloing and vortex dynamics. Edired by O. Boratv, A. Eden & A. Erzan, Lectures Notes in Physics, 92–107

    Google Scholar 

  17. Meneveau, C. & K. R. Sreenivasan. J. Fluid Mech. 224, 429 (1991).

    Article  MATH  ADS  Google Scholar 

  18. Gaudin, E., B. Protas, S. Goujon-Durand, J. Wojciechowski, J. E. Wesfreid. Phys. Rev. E. 57, 9–12 (1998).

    Article  ADS  Google Scholar 

  19. Babiano, A. 2000 On non-homogeneous two-dimensional inverse energy cascade. submited to Phys. of Fluids.

    Google Scholar 

  20. Pedlosky, J. 1987 Geophysical Fluid Dynamics. Springer, Berlin.

    Google Scholar 

  21. Basdevant, C. Legras, B., Sadourny, R. & Beland, M. 1981 A study of barotopic model flows: Intermittency waves and predictability. J. Atmos. Sci 38 2305–2326.

    Google Scholar 

  22. Sadourny, R. & Basdevant, C. 1985 Parameterization of subgrid scale barotropic eddies in quasi-geostrophic models: anticipated potential vorticity method. J. Atmos. Sci. 42, 1353–1363.

    Google Scholar 

  23. Vallis, G.K. & Hua, B.L. 1988 Eddy diffusivity of the Anticipated Potential vorticity method, J. Atmos. Sci., 45, 617–627.

    Google Scholar 

  24. Paret, J. & Tabeling, P. 1998 Intermittency in the 2D inverse cascade of energy: experimental observations. Phys. Fluids, vol 10, 12, 3126–3136.

    Google Scholar 

  25. Babiano, A., Dubrulle, B., Frick, P. 1995 Scaling properties of numerical twodimensional turbulence. Physical Review E, 52, 4, 3719–3729.

    Google Scholar 

  26. Babiano, A., Dubrulle, B., Frick, P. 1997 Some properties of two-dimensional inverse energy cascade dynamics. Physical Review E, 55, 3, 2693–2706.

    Google Scholar 

  27. Babiano, A., Boffetta, G., Provenzale, A. & Vulpiani, A. 1994 Chaotic advection in point vortex models and two-dimensional turbulence. Phys. Fluids A, 6 (7), 2465–2474.

    Google Scholar 

  28. Protas, B., Babiano, A. & Kevlahan K.-R. 1999. On Geometrical Alignment Properties of Two-dimensional Forced Turbulence. Physica D, 128, 169–79.

    Google Scholar 

  29. Larchevêque, M. 1993 Pressure field, vorticity field, and coherent structures in twodimensional incompressible turbulent flows. Theoret. Comput. Fluid Dynamics 5, 215–222.

    Google Scholar 

  30. Hua, B.L., McWilliams J. & Klein, P. 1998 Lagrangian accelerations in geostrophic turbulence. J. Fluid Mech., 366, 87–108.

    Google Scholar 

  31. Lapeyre, G. Klein, P. & Hua, B.L. 1999. Does the tracer gradient vector align with the strain eigenvectors in 2D turbulence? Phys. Fluids, 11, 12, 3729–3737.

    Google Scholar 

  32. Monin, A.S. & Yaglom, A.M. 1975 Statistical Fluid Mechanics. The MIT Press.

    Google Scholar 

  33. Frisch, U. Turbulence. Cambridge University Press, (1995).

    Google Scholar 

  34. Landau, L.D. & E.M. Lifschitz, Fluid Mechanics, 2nd ed. (Pergamon, Oxford, 1987).

    MATH  Google Scholar 

  35. Babiano, A., Basdevant, C. & Sadourny, R. 1985 Structure functions and dispersion laws in two-dimensional turbulence. J. Atmos. Sci. 42, 942–949.

    Google Scholar 

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Babiano, A. (2000). Non-homogeneous/Non-local Two-Dimensional Dynamics. In: Maurel, A., Petitjeans, P. (eds) Vortex Structure and Dynamics. Lecture Notes in Physics, vol 555. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44535-8_1

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  • DOI: https://doi.org/10.1007/3-540-44535-8_1

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67920-2

  • Online ISBN: 978-3-540-44535-7

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