Skip to main content

Linear baroclinic instability in the Martian atmosphere: Primitive equation calculations


In this study, baroclinic-barotropic instability of the Martian atmosphere is studied for a zonal basic state based on Mariner 9 observations, using a spherical linear primitive equation model derived from a method of 3-D normal mode expansion. As a result of solving a matrix eigenvalue problem, a distinctly unstable mode at synoptic to planetary scales was found with a peak growth rate of 2.3 (1/sol) at zonal wavenumbers n = 5 to 6 with an eastward phase speed of 50 (°/sol). The unstable mode has a period of 2.4 sol for n = 3, which agrees well with Viking observations. The geopotential amplitude maximum is located at 50°N near the surface, and the phase tilts westward with height. The structure is similar to baroclinic instability of a Charney mode associated with the subtropical jet on Earth. It is found, however, that the mode on Mars, where the subtropical jet is absent, is not the ordinary Charney mode, but a different one that is referred to as a monopole Charney mode in previous study which is characterized by its overall northward eddy momentum flux.


  • Barnes, J. R., Time spectral analysis of midlatitude disturbances in the Martian atmosphere, J. Atmos. Sci., 37, 2002–2015, 1980.

    Article  Google Scholar 

  • Barnes, J. R., Midlatitude disturbances in the Martian atmosphere: A second Mars year, J. Atmos. Sci., 38, 225–234, 1981.

    Article  Google Scholar 

  • Barnes, J. R., Linear baroclinic instability in the Martian atmosphere, J. Atmos. Sci., 41, 1536–1550, 1984.

    Article  Google Scholar 

  • Barnes, J. R., J. B. Pollack, R. M. Haberle, C. B. Leovy, R. W. Zurek, H. Lee, and J. Schaeffer, Mars atmospheric dynamics as simulated by the NASA Ames general circulation model, 2. Transient baroclinic eddies, J. Geophys. Res., 98, 3125–3148, 1993.

    Article  Google Scholar 

  • Conrath, B. J., Planetary-scale wave structure in the Martian atmosphere, Icarus, 48, 246–255, 1981.

    Article  Google Scholar 

  • Green, J. S. A., A problem in baroclinic instability, Quart. J. Roy. Meteor. Soc., 86, 237–251, 1960.

    Article  Google Scholar 

  • Hartmann, D. L., Baroclinic instability of realistic zonal-mean states to planetary waves, J. Atmos. Sci., 36, 2336–2349, 1979.

    Article  Google Scholar 

  • Hollingsworth, J. L. and J. R. Barnes, Forced stationary planetary waves in Mars’s winter atmosphere, J. Atmos. Sci., 53, 428–448, 1996.

    Article  Google Scholar 

  • Kasahara, A., The linear response of a stratified global atmosphere to tropical thermal forcing, J. Atmos. Sci., 41, 2217–2237, 1984.

    Article  Google Scholar 

  • Leovy, C. B. and Y. Mintz, Numerical simulation of the atmospheric circulation and climate of Mars, J. Atmos. Sci., 26, 1167–1190, 1969.

    Article  Google Scholar 

  • Longuet-Higgins, M. S., The eigenfunction of Laplace’s tidal Equation over a sphere, Phil. Trans. Roy. Soc., London, A262, 511–607, 1968.

    Article  Google Scholar 

  • Michelangeli, D. V. and R. W. Zurek, Barotropic instability of midlatitude zonal jets on Mars, Earth and Venus, J. Atmos. Sci., 44, 2031–2041, 1987.

    Article  Google Scholar 

  • Moriyama, S. and T. Iwashima, A spectral model of the atmospheric general circulation of Mars: A numerical experiment including the effects of the suspended dust and the topography, J. Geophys. Res., 85, 2847–2860, 1980.

    Article  Google Scholar 

  • Pollack, J. B., R. M. Baberle, J. Schaeffer, and H. Lee, Simulation of the general circulation of the Martian atmosphere, I: Polar processes, J. Geophys. Res., 95, 1447–1474, 1990.

    Article  Google Scholar 

  • Seiff, A. and D. B. Kirk, Structure of the atmosphere on Mars in summer at midlatitudes, J. Geophys. Res., 82, 4364–4378, 1977.

    Article  Google Scholar 

  • Tanaka, H. L., A numerical simulation of amplification of low-frequency planetary waves and blocking formations by the upscale energy cascade, Mon. Wea. Rev., 119, 2919–2935, 1991.

    Article  Google Scholar 

  • Tanaka, H. L., Numerical simulation of a life-cycle of atmospheric blocking and the analysis of potential vortisity using a simple barotropic model, J. Meteor. Soc. Japan, 76, 983–1008, 1998.

    Google Scholar 

  • Tanaka, H. L. and E. C. Kung, A study of low-frequency unstable planetary waves in realistic zonal and zonally varying basic states, Tellus, 41A, 179–199, 1989.

    Article  Google Scholar 

  • Wilson, R. J. and K. Hamilton, Comprehensive model simulation of thermal tides in the Martian atmosphere, J. Atmos. Sci., 53, 1290–1326, 1996.

    Article  Google Scholar 

  • Zurek, R. W., Free and forced modes in the Martian atmosphere, J. Geophys. Res., 93, 9452–9462, 1988.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to H. L. Tanaka.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tanaka, H.L., Arai, M. Linear baroclinic instability in the Martian atmosphere: Primitive equation calculations. Earth Planet Sp 51, 225–232 (1999).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: