Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Forward and inverse kinetic energy cascades in Jupiter’s turbulent weather layer


Jupiter’s turbulent weather layer contains phenomena of many different sizes, from local storms up to the Great Red Spot and banded jets. The global circulation is driven by complex interactions with (as yet uncertain) small-scale processes. We have calculated structure functions and kinetic energy spectral fluxes from Cassini observations over a wide range of length scales in Jupiter’s atmosphere. We found evidence for an inverse cascade of kinetic energy from length scales comparable to the first baroclinic Rossby deformation radius up to the global jet scale, but also a forward cascade of kinetic energy from the deformation radius to smaller scales. This second result disagrees with the traditional picture of Jupiter’s atmospheric dynamics, but has some similarities with mesoscale phenomena in the Earth’s atmosphere and oceans. We conclude that the inverse cascade driving Jupiter’s jets may have a dominant energy source at scales close to the deformation radius, such as baroclinic instability.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Sample image of Jupiter’s clouds with jet scale and deformation radius.
Figure 2: Turbulent structure functions in Jupiter’s weather layer.
Figure 3: Energy and enstrophy spectra and spectral fluxes in Jupiter’s weather layer.


  1. 1

    Porco, C. C. et al. Cassini imaging of Jupiter’s atmosphere, satellites, and rings. Science 299, 1541–1547 (2003).

    ADS  Article  Google Scholar 

  2. 2

    Ingersoll, A. P. et al. in Jupiter: The Planet, Satellites and Magnetosphere (eds Bagenal, F., Dowling, T. E. & McKinnon, W. B.) Ch. 6, 105–128 (Cambridge Univ. Press, 2004).

    Google Scholar 

  3. 3

    Vasavada, A. R. & Showman, A. P. Jovian atmospheric dynamics: an update after Galileo and Cassini. Rep. Prog. Phys. 68, 1935–1996 (2005).

    ADS  MathSciNet  Article  Google Scholar 

  4. 4

    Kolmogorov, A. N. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers (English Translation 1991). Proc. R. Soc. Lond. A 434, 9–13 (1941).

    ADS  Article  Google Scholar 

  5. 5

    Fjørtoft, R. On the changes in the spectral distribution of kinetic energy for twodimensional, nondivergent flow. Tellus 5, 225–230 (1953).

    ADS  MathSciNet  Article  Google Scholar 

  6. 6

    Kraichnan, R. Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 1417–1423 (1967).

    ADS  Article  Google Scholar 

  7. 7

    Charney, J. G. Geostrophic turbulence. J. Atmos. Sci. 28, 1087–1095 (1971).

    ADS  Article  Google Scholar 

  8. 8

    Salmon, R. Baroclinic instability and geostrophic turbulence. Geophys. Astrophys. Fluid Dyn. 15, 167–211 (1980).

    ADS  Article  Google Scholar 

  9. 9

    Nastrom, G. D., Gage, K. S. & Jasperson, W. H. Kinetic energy spectrum of large- and mesoscale atmospheric processes. Nature 310, 36–38 (1984).

    ADS  Article  Google Scholar 

  10. 10

    Boer, G. J. & Shepherd, T. G. Large-scale two-dimensional turbulence in the atmosphere. J. Atmos. Sci. 40, 164–184 (1983).

    ADS  Article  Google Scholar 

  11. 11

    Burgess, B. H., Erler, A. R. & Shepherd, T. G. The troposphere-to-stratosphere transition in kinetic energy spectra and nonlinear spectral fluxes as seen in ECMWF analyses. J. Atmos. Sci. 70, 669–687 (2013).

    ADS  Article  Google Scholar 

  12. 12

    Augier, P. & Lindborg, E. A new formulation of the spectral energy budget of the atmosphere, with application to two high-resolution general circulation models. J. Atmos. Sci. 70, 2293–2308 (2013).

    ADS  Article  Google Scholar 

  13. 13

    Dewan, E. M. Stratospheric wave spectra resembling turbulence. Science 204, 832–835 (1979).

    ADS  Article  Google Scholar 

  14. 14

    Lilly, D. K. Stratified turbulence and the mesoscale variability of the atmosphere. J. Atmos. Sci. 40, 749–761 (1983).

    ADS  Article  Google Scholar 

  15. 15

    Tung, K. K. & Orlando, W. W. The k−3 and k−5/3 energy spectrum of atmospheric turbulence: quasigeostrophic two-level model simulation. J. Atmos. Sci. 60, 824–835 (2003).

    ADS  Article  Google Scholar 

  16. 16

    Tulloch, R. & Smith, K. S. A theory for the atmospheric energy spectrum: depth-limited temperature anomalies at the tropopause. Proc. Natl Acad. Sci. USA 103, 14690–14694 (2006).

    ADS  Article  Google Scholar 

  17. 17

    Lindborg, E. Horizontal wavenumber spectra of vertical vorticity and horizontal divergence in the upper troposphere and lower stratosphere. J. Atmos. Sci. 64, 1017–1025 (2007).

    ADS  Article  Google Scholar 

  18. 18

    Vallgren, A., Deusebio, E. & Lindborg, E. Possible explanation of the atmospheric kinetic and potential energy spectra. Phys. Rev. Lett. 107, 268501 (2011).

    ADS  Article  Google Scholar 

  19. 19

    Lindborg, E. Can the atmospheric kinetic energy spectrum be explained by two-dimensional turbulence? J. Fluid Mech. 388, 259–288 (1999).

    ADS  Article  Google Scholar 

  20. 20

    Cho, J. Y. N. & Lindborg, E. Horizontal velocity structure functions in the upper troposphere and lower stratosphere: 1. Observations. J. Geophys. Res. 106, 10223–10232 (2001).

    ADS  Article  Google Scholar 

  21. 21

    King, G. P., Vogelzang, J. & Stoffelen, A. Upscale and downscale energy transfer over the tropical Pacific revealed by scatterometer winds. J. Geophys. Res. 120, 346–361 (2015).

    ADS  Article  Google Scholar 

  22. 22

    King, G. P., Vogelzang, J. & Stoffelen, A. Second-order structure function analysis of scatterometer winds over the tropical Pacific. J. Geophys. Res. 120, 362–383 (2015).

    ADS  Article  Google Scholar 

  23. 23

    Scott, R. B. & Wang, F. Direct evidence of an oceanic inverse kinetic energy cascade from satellite altimetry. J. Phys. Oceanogr. 35, 1650–1666 (2005).

    ADS  Article  Google Scholar 

  24. 24

    Tulloch, R., Marshall, J., Hill, C. & Smith, K. S. Scales, growth rates, and spectral fluxes of baroclinic instability in the ocean. J. Phys. Oceanogr. 41, 1057–1076 (2011).

    ADS  Article  Google Scholar 

  25. 25

    Ingersoll, A. P. et al. Interaction of eddies and mean zonal flow on Jupiter as inferred from Voyager 1 and 2 images. J. Geophys. Res. 86, 8733–8743 (1981).

    ADS  Article  Google Scholar 

  26. 26

    Salyk, C., Ingersoll, A. P., Lorre, J., Vasavada, A. & Del Genio, A. D. Interaction between eddies and mean flow in Jupiter’s atmosphere: analysis of Cassini imaging data. Icarus 185, 430–442 (2006).

    ADS  Article  Google Scholar 

  27. 27

    Galperin, B. et al. Cassini observations reveal a regime of zonostrophic macroturbulence on Jupiter. Icarus 229, 295–320 (2014).

    ADS  Article  Google Scholar 

  28. 28

    Choi, D. S. & Showman, A. P. Power spectral analysis of Jupiter’s clouds and kinetic energy from Cassini. Icarus 216, 597–609 (2011).

    ADS  Article  Google Scholar 

  29. 29

    Maltrud, M. E. & Vallis, G. K. Energy and enstrophy transfer in numerical simulations of two-dimensional turbulence. Phys. Fluids A 5, 1760–1775 (1993).

    ADS  Article  Google Scholar 

  30. 30

    Huang, H.-P., Galperin, B. & Sukoriansky, S. Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere. Phys. Fluids 13, 225–240 (2001).

    ADS  Article  Google Scholar 

  31. 31

    Scott, R. K. & Polvani, L. M. Forced-dissipative shallow-water turbulence on the sphere and the atmospheric circulation of the giant planets. J. Atmos. Sci. 64, 3158–3176 (2007).

    ADS  Article  Google Scholar 

  32. 32

    Porco, C. C. et al. Cassini imaging science: instrument characteristics and anticipated scientific investigations at Saturn. Space Sci. Rev. 115, 363–497 (2004).

    ADS  Article  Google Scholar 

  33. 33

    Vasavada, A. R., Porco, C. C. & The Cassini Imaging Science Team. Cassini Cylindrical-Projection Maps near Jupiter Closest Approach (NASA Planetary Data System, 2008);

  34. 34

    Kolmogorov, A. N. Dissipation of energy in the locally isotropic turbulence (English translation 1991). Proc. R. Soc. Lond. A 434, 15–17 (1941).

    ADS  Article  Google Scholar 

  35. 35

    Davidson, P. A. Turbulence: An Introduction for Scientists and Engineers 2nd edn (Oxford Univ. Press, 2015).

    Google Scholar 

  36. 36

    Blažica, V., Žagar, N., Strajnar, B. & Cedilnik, J. Rotational and divergent kinetic energy in the mesoscale model ALADIN. Tellus A 65, 18918 (2013).

    ADS  Article  Google Scholar 

  37. 37

    Gierasch, P. J. et al. Observation of moist convection in Jupiter’s atmosphere. Nature 403, 628–630 (2000).

    ADS  Article  Google Scholar 

  38. 38

    Ingersoll, A. P., Gierasch, P. J., Banfield, D., Vasavada, A. R. & The Galileo Imaging Team. Moist convection as an energy source for the large-scale motions in Jupiter’s atmosphere. Nature 403, 630–632 (2000).

  39. 39

    Blumen, W. Uniform potential vorticity flow: Part I. Theory of wave interactions and two-dimensional turbulence. J. Atmos. Sci. 35, 774–783 (1978).

    ADS  Article  Google Scholar 

  40. 40

    Held, I. M., Pierrehumbert, R. T., Garner, S. T. & Swanson, K. L. Surface quasi-geostrophic dynamics. J. Fluid Mech. 282, 1–20 (1995).

    ADS  MathSciNet  Article  Google Scholar 

  41. 41

    Tulloch, R. & Smith, K. S. Quasigeostrophic turbulence with explicit surface dynamics: application to the atmospheric energy spectrum. J. Atmos. Sci. 66, 450–467 (2009).

    ADS  Article  Google Scholar 

  42. 42

    Fincham, A. M. & Spedding, G. R. Low cost, high resolution DPIV for measurement of turbulent fluid flow. Exp. Fluids 23, 449–462 (1997).

    Article  Google Scholar 

  43. 43

    Fincham, A. & Delerce, G. Advanced optimization of correlation imaging velocimetry algorithms. Exp. Fluids 29, S13–S22 (2000).

    Article  Google Scholar 

  44. 44

    Young, R. M. B., Read, P. L., Armstrong, D. & Lancaster, A. J. Jupiter Horizontal Wind Velocities at Cloud Level from Cassini [data-set] (Oxford University Research Archive, 2017);

  45. 45

    Williams, E. Aviation Formulary v1.46 (2011);

  46. 46

    Seidelmann, P. K. et al. Report of the IAU/IAG working group on cartographic coordinates and rotational elements: 2006. Celest. Mech. Dyn. Astron. 98, 155–180 (2007).

    ADS  Article  Google Scholar 

  47. 47

    Adams, J. C. & Swarztrauber, P. N. SPHEREPACK 3.0: a model development facility. Mon. Weath. Rev. 127, 1872–1878 (1999).

    ADS  Article  Google Scholar 

  48. 48

    Adams, J. C. & Swarztrauber, P. N. SPHEREPACK 2.0: A Model Development Facility (Technical Report NCAR/TN-436+STR, NCAR, 1997).

  49. 49

    Shepherd, T. G. A spectral view of nonlinear fluxes and stationary-transient interaction in the atmosphere. J. Atmos. Sci. 44, 1166–1178 (1987).

    ADS  Article  Google Scholar 

Download references


Support for R.M.B.Y. was provided by UK STFC Grant ST/K00106X/1. This work was supported in part by the US National Science Foundation under Grant No. NSF PHY11-25915. We are grateful to the Leverhulme Trust for their support of the International Network on Waves and Turbulence. Raw images were made available by the Cassini Imaging Science Team via the NASA PDS Atmospheres Node. Data sets C11 and S06 were kindly provided by D. Choi and C. Salyk. We wish to thank P. Davidson, B. Galperin, G. King, B. Marston, M. McIntyre, H. Scolan, F. Tabataba-Vakili, S. Thomson and A. Valeanu for useful discussions.

Author information




R.M.B.Y. wrote the code to calculate the structure functions and spectral fluxes, and performed the calculations. R.M.B.Y. wrote the bulk of the paper with sections on background and interpretation written by P.L.R. Both authors designed the research, decided on the methods used, and discussed the results.

Corresponding author

Correspondence to Roland M. B. Young.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 1437 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Young, R., Read, P. Forward and inverse kinetic energy cascades in Jupiter’s turbulent weather layer. Nature Phys 13, 1135–1140 (2017).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing