• Bretherton, F. P., 1966: Critical layer instability in baroclinic flows. Quart. J. Roy. Meteor. Soc.,92, 325–333.

  • Cehelsky, P., and K.-K. Tung, 1991: Nonlinear baroclinic adjustment. J. Atmos. Sci.,48, 1930–1947.

  • Charney, J. G., 1947: The dynamics of long waves in a baroclinic westerly current. J. Meteor.,4, 135–162.

  • ——, and P. G. Drazin, 1961: Propagation of planetary scale disturbances from the lower into the upper atmosphere. J. Geophys. Res.,66, 83–110.

  • ——, and M. E. Stern, 1962: On the instability of internal baroclinic jets in a rotating atmosphere. J. Atmos. Sci.,19, 159–172.

  • Eady, E. T., 1949: Long waves and cyclone waves. Tellus,1, 33–52.

  • Fullmer, J. W. A., 1982a: Calculations of the quasi-geostrophic PV gradient from climatological data. J. Atmos. Sci.,39, 1873–1877.

  • ——, 1982b: The baroclinic instability of highly structured one-dimensional basic states. J. Atmos. Sci.,39, 2371–2378.

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

  • Grotjahn, R., 1979: Cyclone development along weak thermal fronts. J. Atmos. Sci.,36, 2049–2074.

  • Gutowski, W. J., 1985: Baroclinic adjustment and mid-latitude temperature profiles. J. Atmos. Sci.,42, 1733–1745.

  • ——, L. E. Branscome, and D. A. Stewart, 1989: Mean flow adjustment during life cycles of baroclinic waves. J. Atmos. Sci.,46, 1724–1737.

  • Kuo, H. L., 1979: Baroclinic instabilities of linear and jet profiles in the atmosphere. J. Atmos. Sci.,36, 2360–2378.

  • Lindzen, R. S., 1993: Baroclinic neutrality and the tropopause. J. Atmos. Sci.,50, 1148–1151.

  • ——, 1994a: The effect of concentrated PV gradients on stationary waves. J. Atmos. Sci.,51, 3455–3466.

  • ——, 1994b: The Eady problem for a basic state with zero PV gradients but β ≠ 0. J. Atmos. Sci.,51, 3221–3226.

  • ——, and B. F. Farrell, 1980a: The role of polar regions in global climate, and the parameterization of global heat transport. Mon. Wea. Rev.,108, 2064–2079.

  • ——, and ——, 1980b: A simple approximate result for the maximum growth rate of baroclinic instabilities. J. Atmos. Sci.,37, 1648–1654.

  • ——, ——, and K. K. Tung, 1980: The concept of wave overreflection and its application to baroclinic instability. J. Atmos. Sci.,37, 44–63.

  • Morgan, M. C., 1995: An observationally and dynamically determined basic state for the study of synoptic-scale waves. Ph.D. thesis, Massachusetts Institute of Technology, 123 pp. [Available from PAOC, 54-1424, Massachusetts Institute of Technology, Cambridge, MA 02139.].

  • Randel, W. J., and J. L. Stanford, 1985: The observed life cycle of a baroclinic instability. J. Atmos. Sci.,42, 1364–1373.

  • Rhines, P. B., and W. R. Young, 1982: Homogenization of potential vorticity in planetary gyres. J. Fluid Mech.,122, 347–367.

  • Simmons, A. J., and B. J. Hoskins, 1978: The life cycles of some nonlinear baroclinic waves. J. Atmos. Sci.,35, 414–432.

  • Snyder, C. M., and R. S. Lindzen, 1988: Upper-level baroclinic instability. J. Atmos. Sci.,45, 2445–2459.

  • Stone, P. H., 1978: Baroclinic adjustment. J. Atmos. Sci.,35, 561–570.

  • ——, and L. Branscome, 1992: Diabatically forced nearly inviscid eddy regimes. J. Atmos. Sci.,49, 2446–2459.

  • ——, and B. Nemet, 1996: Baroclinic adjustment: A comparison between theory, observation, and models. J. Atmos. Sci.,53, 1663–1674.

  • Sun, D. Z., and R. S. Lindzen, 1994: A PV view of the zonal mean distribution of temperature and wind in the extratropical troposphere. J. Atmos. Sci.,51, 757–772.

  • Thorncroft, C. D., B. J. Hoskins, and M. E. McIntyre, 1993: Two paradigms of baroclinic-wave life-cycle behaviour. Quart. J. Roy. Meteor. Soc.,119, 17–55.

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The Effect of Basic-State Potential Vorticity Gradients on the Growth of Baroclinic Waves and the Height of the Tropopause

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  • 1 Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

The stability characteristics of normal mode perturbations on idealized basic states that have meridional potential vorticity (PV) gradients that are zero in the troposphere, very large at the tropopause, and order β in the stratosphere are checked. The results are compared to the corresponding models that have a lid at the tropopause. The dispersion relations and the vertical structures of the modes are similar in the two models, thus confirming the relevance of the Eady problem to unbounded atmospheres. The effect of replacing the lid with a more realistic tropopause is to complicate the interaction of tropopause and surface waves, such as to inhibit phase locking for a range of wavenumbers. This causes the short-wave cutoff of the Eady model to move to longer waves. Also, there is a slight destabilization of the long waves, which have large amplitudes in the stratosphere.

The effect of gradually changing the tropospheric PV gradients from zero (Eady-type profile) to β (Green- type profile) on the stability of normal modes is checked. The dispersion relations show a smooth transition from the Green profiles to the Eady profiles, and a short-wave cutoff is gradually formed.

Finally, the possibility of neutralizing the atmosphere through the short-wave cutoff of the Eady model by lifting the tropopause while keeping PV gradients zero in the troposphere is examined. It is found that instability depends on some minimal amount of tunneling of waves between the surface and the tropopause. The amount of tunneling depends on the vertical integral of N in the troposphere. It is necessary for ∫ N dz to increase for the short-wave cutoff to move to longer waves. For reasonable Brunt–Vä∩älä frequency profiles, lifting the tropopause causes the short-wave cutoff to move to longer wavelengths, but the details are sensitive to boundary values of N2 and wind shear.

Corresponding author address: Dr. Richard S. Lindzen, Dept. of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Rm. 54-1720, Cambridge, MA 02139.

Email: rlindzen@mit.edu

Abstract

The stability characteristics of normal mode perturbations on idealized basic states that have meridional potential vorticity (PV) gradients that are zero in the troposphere, very large at the tropopause, and order β in the stratosphere are checked. The results are compared to the corresponding models that have a lid at the tropopause. The dispersion relations and the vertical structures of the modes are similar in the two models, thus confirming the relevance of the Eady problem to unbounded atmospheres. The effect of replacing the lid with a more realistic tropopause is to complicate the interaction of tropopause and surface waves, such as to inhibit phase locking for a range of wavenumbers. This causes the short-wave cutoff of the Eady model to move to longer waves. Also, there is a slight destabilization of the long waves, which have large amplitudes in the stratosphere.

The effect of gradually changing the tropospheric PV gradients from zero (Eady-type profile) to β (Green- type profile) on the stability of normal modes is checked. The dispersion relations show a smooth transition from the Green profiles to the Eady profiles, and a short-wave cutoff is gradually formed.

Finally, the possibility of neutralizing the atmosphere through the short-wave cutoff of the Eady model by lifting the tropopause while keeping PV gradients zero in the troposphere is examined. It is found that instability depends on some minimal amount of tunneling of waves between the surface and the tropopause. The amount of tunneling depends on the vertical integral of N in the troposphere. It is necessary for ∫ N dz to increase for the short-wave cutoff to move to longer waves. For reasonable Brunt–Vä∩älä frequency profiles, lifting the tropopause causes the short-wave cutoff to move to longer wavelengths, but the details are sensitive to boundary values of N2 and wind shear.

Corresponding author address: Dr. Richard S. Lindzen, Dept. of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Rm. 54-1720, Cambridge, MA 02139.

Email: rlindzen@mit.edu

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