Skip to main content
Log in

On the locality of the kinetic energy transfer in a wave space

  • Published:
Izvestiya, Physics of the Solid Earth Aims and scope Submit manuscript

Abstract

For the model of thermal turbulence in the Boussinesq approximation with heating from below a change in the structure of the nonlinear interaction of the harmonics of the velocity field with the appearance of rotation is examined. The parameters of convection with rotation are chosen in such a way to correspond to the typical regimes in the models of the planetary dynamo. For such regimes, the structure of the triadic mechanism of the kinetic energy transfer through the spectrum is investigated.

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.

Similar content being viewed by others

References

  1. A. Alexakis, P. D. Mininni, and A. Pouquet, “Shell to Shell Energy Transfer in MHD. I. Steady State Turbulence,” Phys. Rev., V.E 72 046301–046309 (2005).

    Google Scholar 

  2. A. Alexakis, P. D. Mininni, and A. Pouquet, “Turbulent Cascades, Transfer, and Scale Interactions in Magnetohydrodynamics,” New Journal of Pysics, 298(9), 1–20 (2007).

    Google Scholar 

  3. G. K. Batchelor, The Theory of Homogeneous Turbulence (Cambridge University Press, Cambridge, 1953) pp. 1–195.

    Google Scholar 

  4. F. H. Busse, “Thermal Instabilities in Rapidly Rotating Systems,” J. Fluid Mech., 44, 441–460 (1970).

    Article  Google Scholar 

  5. F. Cattaneo, O. Emonet, and N. Weis, “On the Interaction between Convection and Magnetic Fields,” Ap. J., 588, 1183–1198 (2003).

    Article  Google Scholar 

  6. S. Chandrasekhar, Hydrodynamics and Hydromagnetic Stability, (Dover Publications. Inc., New York, 1981), pp. 1–654.

    Google Scholar 

  7. O. Debliquy, M. Verma, and D. Carati, “Energy Fluxes and Shell-to-Shell Transfers in Three-Dimensional Decaying Magnetohydrodynamic Turbulence,” Physics of Plasmas, 12, 042309-1–042309-10 (2005).

    Article  Google Scholar 

  8. U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge University Press., Cambridge, 1995) pp. 1–296.

    Google Scholar 

  9. C. A. Jones, “Convection-Driven Geodynamo Models,” Phil. Trans. R. Soc. London. A358 873–897 (2000).

    Google Scholar 

  10. C. A. Jones, P. H. Roberts, “Convection Driven Dynamos in a Rotating Plane Layer,” J. Fluid Mechanics, 404, 311–343 (2000).

    Article  Google Scholar 

  11. R. H. Kraichnan and D. Montgomery, “Two-Dimensional Turbulence,” Rep. Prog. Phys. 43, 547–619 (1980).

    Article  Google Scholar 

  12. M. Meneguzzi and A. Pouquet, “Turbulent Dynamos Driven by Convection,” J. Fluid Mech., 205, 297–318 (1989).

    Article  Google Scholar 

  13. S. A. Orszag, “Numerical Simulation of Incompressible Flows within Simple Boundaries. I. Galerkin (Spectral) Representations,” Stud. Appl. Math., L(51), 293–327 (1971).

    Google Scholar 

  14. J. Pedlosky, Geophysical Fluid Dynamics (Springer-Verlag, New York, 1987) pp. 1–710.

    Google Scholar 

  15. M. Yu. Reshetnyak, “Cascade Processes in Magnetostrophic Turbulence,” Dokl. RAN (Geophysics), 420(4) 527–531 (2008a).

    Google Scholar 

  16. M. Yu. Reshetnyak, “Heat Convection and Dynamo with the Fast Rotation Motion,” Fiz. Zemli. 8, 23–32 (2007).

    Google Scholar 

  17. M. Yu. Reshetnyak, “Some Properties of Cyclonic Turbulence in the Liquid Earth Core,” Geomagnetism and Aeronomy, 48(3) 416–423 (2008b).

    Article  Google Scholar 

  18. M. Reshetnyak and B. Steffen, “Shell Models in Rapidly Rotating Dynamo Systems,” Numerical Methods and Programming, 7 85–92 (2006). (http://www.srcc.msu.su/nummeth/english/index.html)

    Google Scholar 

  19. H. A. Rose and P. I. Sulem, “Fully Developed Turbulence and Statistical Mechanics,” J. Physique., 39, 441–484 (1978).

    Google Scholar 

  20. P. Tabeling, “Two-Dimensional Turbulence: a Physicist Approach,” Phys. Reports, 362 1–62 (2002).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © M.Yu. Reshetnyak, 2009, published in Fizika Zemli, 2009, No. 8, pp. 83–90.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Reshetnyak, M.Y. On the locality of the kinetic energy transfer in a wave space. Izv., Phys. Solid Earth 45, 701–708 (2009). https://doi.org/10.1134/S1069351309080096

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1069351309080096

Key words

PACS numbers

Navigation