Cover Journal of the Atmospheric Sciences
Journal of the Atmospheric Sciences

  • Bishop, C. H., and A. J. Thorpe, 1994: Potential vorticity and the electrostatics analogy: Quasi-geostrophic theory. Quart. J. Roy. Meteor. Soc.,120, 713–731.

  • Blackmon, M. L., 1976: A climatological spectral study of the 500 mb geopotential height of the Northern Hemisphere. J. Atmos. Sci.,33, 1607–1623.

  • ——, Y.-H. Lee, and J. M. Wallace, 1984a: Horizontal structure of 500 mb height fluctuations with long, intermediate and short time scales. J. Atmos. Sci.,41, 961–979.

  • ——, ——, ——, and H.-H. Hsu, 1984b: Time variation of 500 mb height fluctuations with long, intermediate and short time scales as deduced from lag-correlation statistics. J. Atmos. Sci.,41, 981–991.

  • Briggs, R. J., 1964: Electron Stream Interaction with Plasma. Research Monogr., No. 29, The MIT Press, 187 pp.

  • Chang, E. K. M., 1992: Resonating neutral modes of the Eady model. J. Atmos. Sci.,49, 2452–2463.

  • ——, 1993: Downstream development of baroclinic waves as inferred from regression analysis. J. Atmos. Sci.,50, 2038–2053.

  • Davies, H. C., and C. H. Bishop, 1994: Eady edge waves and rapid development. J. Atmos. Sci.,51, 1930–1946.

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

  • Farrell, B. F., 1984: Modal and non-modal baroclinic waves. J. Atmos. Sci.,41, 668–673.

  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Hirota, I., K. Yamada, and K. Sato, 1995: Medium-scale travelling waves over the North Atlantic J. Meteor. Soc. Japan,73, 1175–1179.

  • Holton, J. R., 1992: An Introduction to Dynamic Meteorology. Academic Press, 507 pp.

  • Hoskins, B. J., and P. J. Valdes, 1990: On the existence of storm-tracks. J. Atmos. Sci.,47, 1854–1864.

  • ——, M. E. McIntyre, and W. Robinson, 1985: On the use and significance of isentropic potential vorticity maps. Quart. J. Roy. Meteor. Soc.,111, 877–946.

  • James, I. N., 1994: Introduction to Circulating Atmospheres. Cambridge University Press, 422 pp.

  • Lau, N. C., and J. M. Wallace, 1979: On the distribution of horizontal transports by transient eddies in the Northern Hemisphere wintertime circulation. J. Atmos. Sci.,36, 1844–1863.

  • Lee, S., and I. M. Held, 1993: Baroclinic wave packets in models and observations. J. Atmos. Sci.,50, 1413–1428.

  • Lim, G. H., and J. M. Wallace, 1991: Structure and evolution of baroclinic waves as inferred from regression analysis. J. Atmos. Sci.,48, 1718–1732.

  • Lindzen, R. S., 1994: The Eady problem for a basic state with zero PV gradient but β ≠ 0. J. Atmos. Sci.,51, 3221–3226.

  • Merkine, L., 1977: Convective and absolute instability of baroclinic eddies. Geophys. Astrophys. Fluid Dyn.,9, 129–157.

  • Müller, J. C., H. C. Davies, and C. Shar, 1989: An unsung mechanism for frontogenesis and cyclogenesis. J. Atmos. Sci.,46, 3664–3672.

  • Parker, D. J., 1998: Secondary frontal waves in the North Atlantic region: A dynamical perspective of current ideas. Quart. J. Roy. Meteor. Soc.,124, 829–856.

  • Pedlosky, J., 1964: An initial value problem in the theory of baroclinic instability. Tellus,16, 12–17.

  • Pierrehumbert, R. T., 1984: Local and global baroclinic instability of zonally varying flow. J. Atmos. Sci.,41, 2141–2162.

  • Sato, K., H. Eito, and I. Hirota, 1993: Medium-scale travelling waves over the North Atlantic. J. Meteor. Soc. Japan,71, 427–436.

  • Shepherd, T. G., 1985: Time development of small disturbances to plane Couette flow. J. Atmos. Sci.,42, 1868–1871.

  • Swanson, K. L., and R. T. Pierrehumbert, 1995: Potential vorticity homogenization and stationary waves. J. Atmos. Sci.,52, 990–994.

  • Thorncroft, C. D., and B. J. Hoskins, 1990: Frontal cyclogenesis. J. Atmos. Sci.,47, 2317–2336.

  • Yamamoru, M., K. Sato, and I. Hirota, 1997: A study of the seasonal variation of upper tropospheric medium-scale waves over east Asia based on regional climate model data. J. Meteor. Soc. Japan,75, 13–22.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 72 72 1
PDF Downloads 4 4 0
Editorial Type:
Article

Apparent Absolute Instability and the Continuous Spectrum

C. H. Bishop1 and E. Heifetz2
View More View Less
  • 1 Department of Meteorology, The Pennsylvania State University, University Park, Pennsylvania
  • | 2 Department of Earth and Planetary Sciences, Harvard University, Cambridge, Massachusetts
Print Publication:
01 Nov 2000
DOI:
https://doi.org/10.1175/1520-0469(2000)057<3592:AAIATC>2.0.CO;2
Page(s):
3592–3608
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

The role of the continuous spectrum and its associated potential vorticity (PV) in absolute instability are investigated in the context of a semi-infinite version of Eady’s basic state. This flow crudely resembles the zonally averaged midlatitude atmosphere. The disturbances are composed of a zero PV part and a nonzero PV part. A closed form analytic solution is described that features a localized wave packet whose streamfunction field expands and amplifies in an absolutely unstable way. However, since an examination of the PV field associated with this disturbance reveals that the linear amplification of the localized streamfunction wave packet is induced by a nonlocalized PV field, it is clear that the seed for the expansion of the streamfunction wave packet lies not within the wave packet but upstream of the wave packet. While this precise analytic solution allows for the identification of the upstream PV anomalies, any sort of measurement error would render these upstream PV anomalies invisible. Thus, observations would be incapable of distinguishing an absolute instability seeded by PV anomalies generated within the confines of the streamfunction wave packet from the absolute instability described by the authors’ solution.

The general initial value solution is analyzed, and it is found that this apparent absolute instability is not a peculiarity of this particular solution. Absolutely unstable wave packets will be “naturally selected” over geophysically relevant timescales to dominate the flows that emerge from random disturbances to the idealized basic state. In Eady’s basic state, which is bounded aloft by a rigid lid, the natural selection mechanism only operates at wavelengths at which the normal modes of Eady’s basic state are neutral. It is suggested that an atmospheric counterpart of this natural selection process may be responsible for the medium-scale upper- and lower-tropospheric waves that have recently been identified in the observational record.

The authors prove that the group velocity of a streamfunction field attributable to eastward moving PV anomalies may, in fact, be westward.

Corresponding author address: Dr. C. H. Bishop, Dept. of Meteorology, The Pennsylvania State University, 520 Walker Building, University Park, PA 16802.

Email: cbishop@essc.psu.edu

Abstract

The role of the continuous spectrum and its associated potential vorticity (PV) in absolute instability are investigated in the context of a semi-infinite version of Eady’s basic state. This flow crudely resembles the zonally averaged midlatitude atmosphere. The disturbances are composed of a zero PV part and a nonzero PV part. A closed form analytic solution is described that features a localized wave packet whose streamfunction field expands and amplifies in an absolutely unstable way. However, since an examination of the PV field associated with this disturbance reveals that the linear amplification of the localized streamfunction wave packet is induced by a nonlocalized PV field, it is clear that the seed for the expansion of the streamfunction wave packet lies not within the wave packet but upstream of the wave packet. While this precise analytic solution allows for the identification of the upstream PV anomalies, any sort of measurement error would render these upstream PV anomalies invisible. Thus, observations would be incapable of distinguishing an absolute instability seeded by PV anomalies generated within the confines of the streamfunction wave packet from the absolute instability described by the authors’ solution.

The general initial value solution is analyzed, and it is found that this apparent absolute instability is not a peculiarity of this particular solution. Absolutely unstable wave packets will be “naturally selected” over geophysically relevant timescales to dominate the flows that emerge from random disturbances to the idealized basic state. In Eady’s basic state, which is bounded aloft by a rigid lid, the natural selection mechanism only operates at wavelengths at which the normal modes of Eady’s basic state are neutral. It is suggested that an atmospheric counterpart of this natural selection process may be responsible for the medium-scale upper- and lower-tropospheric waves that have recently been identified in the observational record.

The authors prove that the group velocity of a streamfunction field attributable to eastward moving PV anomalies may, in fact, be westward.

Corresponding author address: Dr. C. H. Bishop, Dept. of Meteorology, The Pennsylvania State University, 520 Walker Building, University Park, PA 16802.

Email: cbishop@essc.psu.edu

Save