• Ambaum, M. A., 1997: Isentropic formation of the tropopause. J. Atmos. Sci.,54, 555–568.

  • ——, and W. T. M. Verleley, 1995: Orography in a contour dynamics model of large-scale atmospheric flow. J. Atmos. Sci.,52, 2643–2662.

  • Andrews, D. G., and M. E. McIntyre, 1978: An exact theory of nonlinear waves on a Lagrangian flow. J. Fluid Mech.,89, 609–646.

  • Arnol’d, V. I., 1966: On an a priori estimate in the theory of hydrodynamical stability (in Russian). Isv. Vyssh. Uchebn. Zaved. Math.,54, 3–4.

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

  • Branstator, G., 1987: A striking example of the atmosphere’s leading traveling pattern. J. Atmos. Sci.,44, 2310–2323.

  • ——, 1995: Organization of storm track anomalies by recurring low-frequency circulation anomalies. J. Atmos. Sci.,52, 207–226.

  • Bretherton, F. P., and C. J. R. Garrett, 1968: Wave trains in inhomogeneous moving media. Proc. Roy. Soc. London,302A, 529–554.

  • Charney, J. G., and J. G. Devore, 1979: Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci.,36, 1205–1216.

  • Chen, W. Y., and H. M. van den Dool, 1997: Asymmetric impact of tropical SST anomalies on atmospheric internal variability over the North Pacific. J. Atmos. Sci.,54, 725–740.

  • Dritschel, D. G., 1988: Contour surgery: A topological reconnection scheme for extended integrations using contour dynamics. J. Comput. Phys.,77, 240–266.

  • ——, 1989a: Contour dynamics and contour surgery: Numerical algorithms for extended, high-resolution modeling of vortex dynamics in two-dimensional, inviscid, incompressible flows. Comput. Phys. Rep.,77, 240–266.

  • ——, 1989b: On the stabilization of a two-dimensional vortex by adverse shear. J. Fluid Mech.,206, 193–221.

  • Farrell, B., and I. Watterson, 1985: Rossby waves in opposing currents. J. Atmos. Sci.,42, 1746–1756.

  • Grimshaw, R., 1984: Wave action and wave–mean flow interaction, with application to stratified shear flows. Annu. Rev. Fluid. Mech.,16, 11–44.

  • Held, I. M., 1983: Stationary and quasi-stationary eddies in the extratropical troposphere: Theory. Large-Scale Dynamical Processes in the Atmosphere, B. Hoskins and R. Pearce, Eds., Academic Press, 127–168.

  • ——, and A. Y. Hou, 1980: Nonlinear axially symmetric circulations in a nearly inviscid atmosphere. J. Atmos. Sci.,37, 515–533.

  • ——, S. W. Lyons, and S. Nigam, 1989: Transients and the extratropical response to El Niño. J. Atmos. Sci.,46, 163–174.

  • Hoskins, B. J., and T. Ambrizzi, 1993: Rossby wave propagation on a realistic longitudinally varying flow. J. Atmos. Sci.,50, 1661–1671.

  • ——, and D. J. Karoly, 1981: The steady linear response of a spherical atmosphere to thermal and orographic forcing. J. Atmos. Sci.,38, 1179–1196.

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

  • Kushner, P. J., and I. M. Held, 1999: Potential vorticity thickness fluxes and wave–mean flow interaction. J. Atmos. Sci.,56, 948–958.

  • Kushnir, Y., 1987: Retrograding wintertime low-frequency disturbance over the North Pacific Ocean. J. Atmos. Sci.,44, 2727–2742.

  • McIntyre, M. E., and T. G. Shepherd, 1987: An exact local conservation theorem for finite amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and Arnol’d’s stability theorems. J. Fluid Mech.,181, 527–565.

  • Nakamura, M., and R. A. Plumb, 1994: The effects of flow asymmetry on the direction of Rossby wave breaking. J. Atmos. Sci.,51, 2031–2045.

  • Newman, M., P. D. Sardeshmukh, and C. Penland, 1997: Stochastic forcing of the wintertime extratropical flow. J. Atmos. Sci.,54, 435–455.

  • Pieters, D., and W. D. Waugh, 1996: Influence of barotropic shear on the poleward advection of upper-tropospheric air. J. Atmos. Sci.,53, 3013–3031.

  • Plumb, R. A., 1981: Instability of the distorted polar night vortex: A theory of sudden stratospheric warmings. J. Atmos. Sci.,38, 2514–2531.

  • Polvani, L. M., and R. A. Plumb, 1992: Rossby wave breaking, filamentation, and secondary vortex formation: The dynamics of a perturbed vortex. J. Atmos. Sci.,49, 462–476.

  • ——, N. J. Zabuski, and G. R. Flierl, 1989: Two-layer geostrophic vortex dynamics. Part 1: Upper layer V-states and merger. J. Fluid Mech.,205, 215–242.

  • Rinne, J., and H. Jarvinen, 1993: Estimation of the Cressman term for a barotropic model through optimization with the use of an adjoint model. Mon. Wea. Rev.,121, 825–833.

  • Rivest, C., and B. F. Farrell, 1992: Upper-tropospheric synoptic-scale waves. Part I: Maintenance as Eady normal modes. J. Atmos. Sci.,49, 2108–2119.

  • Sanders, F., 1988: Life history of mobile troughs in the upper westerlies. Mon. Wea. Rev.,116, 2629–2648.

  • Simmons, A. J., J. M. Wallace, and G. Branstator, 1983: Barotropic wave propagation and instability, and atmospheric teleconnection patterns. J. Atmos. Sci.,40, 1363–1392.

  • Swanson, K. L., P. J. Kushner, and I. M. Held, 1997: Dynamics of barotropic storm tracks. J. Atmos. Sci.,54, 791–810.

  • Verkeley, W. T. M., 1994: Tropopause dynamics and planetary waves. J. Atmos. Sci.,51, 509–529.

  • Waugh, D. W., 1992: The efficiency of symmetric vortex merger. Phys. Fluids A,4, 1745.

  • ——, and D. G. Dritschel, 1991: The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models. J. Fluid Mech.,231, 575–598.

  • ——, L. M. Polvani, and R. A. Plumb, 1994: Nonlinear barotropic response to localized topographic forcing: Formation of a “tropical surf zone” and its effect on interhemispheric propagation. J. Atmos. Sci.,51, 1401–1416.

  • Webster, P. J., and H.-R. Chang, 1988: Equatorial energy accumulation and emanation regions: Impact of a zonally varying basic state. J. Atmos. Sci.,45, 803–829.

  • Whitaker, J. S., and P. D. Sardeshmukh, 1998: A linear theory of extratropical synoptic eddy statistics. J. Atmos. Sci.,55, 237–258.

  • Whitham, G. B., 1965: A general approach to linear and non-linear dispersive waves using a Lagrangian. J. Fluid Mech.,22, 273–283.

  • ——, 1974: Linear and Nonlinear Waves. Wiley, 636 pp.

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Stationary Wave Accumulation and the Generation of Low-Frequency Variability on Zonally Varying Flows

K. L. SwansonUniversity of Wisconsin—Milwaukee, Milwaukee, Wisconsin

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Abstract

A potent mechanism for the generation of low-frequency atmospheric variability on vortex basic states consisting of a single potential vorticity jump, or contour, separating two regions of uniform equivalent barotropic potential vorticity is described. Such basic states represent in a simple manner the potential vorticity distribution of the extratropical upper troposphere. It is shown that the group velocity for stationary waves propagating on such states can vanish for realistic zonal variations in the basic-state flow along the vortex edge, leading to local exponential disturbance growth due to the accumulation of wave action. Further, pseudo-energy stability criteria are derived that suggest that exponentially growing global disturbances are possible for sufficiently strong zonal variations in the flow along the vortex edge.

These predictions are examined using linear and nonlinear initial value problem calculations. For wavenumber-1 flow variations in the basic-state zonal flow along the vortex edge, no global instability occurs. However, strong local disturbance growth in response to weak stationary forcing does occur and can lead to irreversible deformation of the vortex. For wavenumber-2 and higher variations in the basic-state zonal flow along the vortex edge, global instability occurs if the stability criteria is violated. These instabilities have peak dimensional e-folding times on the order of one week, with faster growth rates corresponding to stronger zonal variations in the flow along the vortex edge. Quantization of the zonal scale of amplifying disturbances occurs, indicating disturbance resonance with the underlying zonal variations in the basic-state flow along the vortex edge. In the nonlinear regime, longer wavelength disturbances lead to large amplitude periodic fluctuations of the vortex. Intermediate wavelength disturbances are shown to yield suprisingly realistic blocking events, while short wavelength disturbances saturate at amplitudes too small to change the overall structure of the vortex.

The pervasiveness of instability in this simple system suggests similar processes may be important for blocking transitions and the generation of low-frequency variability in the extratropical atmosphere. Preliminary results from the National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis show that the climatological 330-K isentropic potential vorticity is accurately characterized as the time average of a fluctuating single-contour vortex. Wave action conservation on basic states constructed using dynamical fields on the 330-K isentropic surface reproduces observed shifts in low-frequency variability that occur during the El Niño cycle. Further, these shifts lead to transient-driven time mean flow anomalies that have a teleconnection pattern-like structure, despite the fact that meridional propagation of waves is forbidden in this system. The ability of this system to accurately simulate diverse atmospheric phenomena as well as explain certain aspects of upper-tropospheric dynamics suggests that it may provide a powerful new paradigm with which to view low-frequency dynamics in the climate system.

Corresponding author address: Kyle Swanson, Department of Mathematical Sciences, University of Wisconsin—Milwaukee, Milwaukee, WI 53201.

Email: kswanson@csd.uwm.edu

Abstract

A potent mechanism for the generation of low-frequency atmospheric variability on vortex basic states consisting of a single potential vorticity jump, or contour, separating two regions of uniform equivalent barotropic potential vorticity is described. Such basic states represent in a simple manner the potential vorticity distribution of the extratropical upper troposphere. It is shown that the group velocity for stationary waves propagating on such states can vanish for realistic zonal variations in the basic-state flow along the vortex edge, leading to local exponential disturbance growth due to the accumulation of wave action. Further, pseudo-energy stability criteria are derived that suggest that exponentially growing global disturbances are possible for sufficiently strong zonal variations in the flow along the vortex edge.

These predictions are examined using linear and nonlinear initial value problem calculations. For wavenumber-1 flow variations in the basic-state zonal flow along the vortex edge, no global instability occurs. However, strong local disturbance growth in response to weak stationary forcing does occur and can lead to irreversible deformation of the vortex. For wavenumber-2 and higher variations in the basic-state zonal flow along the vortex edge, global instability occurs if the stability criteria is violated. These instabilities have peak dimensional e-folding times on the order of one week, with faster growth rates corresponding to stronger zonal variations in the flow along the vortex edge. Quantization of the zonal scale of amplifying disturbances occurs, indicating disturbance resonance with the underlying zonal variations in the basic-state flow along the vortex edge. In the nonlinear regime, longer wavelength disturbances lead to large amplitude periodic fluctuations of the vortex. Intermediate wavelength disturbances are shown to yield suprisingly realistic blocking events, while short wavelength disturbances saturate at amplitudes too small to change the overall structure of the vortex.

The pervasiveness of instability in this simple system suggests similar processes may be important for blocking transitions and the generation of low-frequency variability in the extratropical atmosphere. Preliminary results from the National Centers for Environmental Prediction–National Center for Atmospheric Research reanalysis show that the climatological 330-K isentropic potential vorticity is accurately characterized as the time average of a fluctuating single-contour vortex. Wave action conservation on basic states constructed using dynamical fields on the 330-K isentropic surface reproduces observed shifts in low-frequency variability that occur during the El Niño cycle. Further, these shifts lead to transient-driven time mean flow anomalies that have a teleconnection pattern-like structure, despite the fact that meridional propagation of waves is forbidden in this system. The ability of this system to accurately simulate diverse atmospheric phenomena as well as explain certain aspects of upper-tropospheric dynamics suggests that it may provide a powerful new paradigm with which to view low-frequency dynamics in the climate system.

Corresponding author address: Kyle Swanson, Department of Mathematical Sciences, University of Wisconsin—Milwaukee, Milwaukee, WI 53201.

Email: kswanson@csd.uwm.edu

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