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- Author or Editor: A. Sutera x
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Abstract
The authors search the stationary solutions of the barotropic vorticity equation in spherical coordinates by numerically solving the equations with the Newton–Keller pseudoarclength continuation method. The solutions consist of planetary-scale Rossby waves superimposed on zonal wind profiles and forced by sinusoidal orography in near-resonance conditions. By varying the zonal wind strength across resonance, it is shown that multiple solutions with different wave amplitudes can be found: for small forcing and dissipation, the solution curve is the well-known bended resonance. The comparison between numerical results and theoretical predictions by a previously developed weakly nonlinear theory is successfully attempted.
The authors then extend the barotropic, weakly nonlinear theory to stationary Rossby waves forced by large-scale orography and dissipated by Ekman friction at the surface, in the framework of the quasigeostrophic model continuous in the vertical direction. The waves are superimposed on vertical profiles of zonal wind and stratification parameters taken from observations of the wintertime Northern Hemisphere circulation. In near-resonant conditions, the weakly nonlinear theory predicts multiple amplitude equilibration of the eddy field for a fixed vertical profile of the zonal wind. The authors discuss the energetics of the stationary waves and show that the form drag and Ekman dissipation can be made very small even if realistic values of the parameters are taken, at variance with the barotropic case.
This model is proposed as the theoretical base for such phenomena as atmospheric blocking, bimodality, and weather regimes.
Abstract
The authors search the stationary solutions of the barotropic vorticity equation in spherical coordinates by numerically solving the equations with the Newton–Keller pseudoarclength continuation method. The solutions consist of planetary-scale Rossby waves superimposed on zonal wind profiles and forced by sinusoidal orography in near-resonance conditions. By varying the zonal wind strength across resonance, it is shown that multiple solutions with different wave amplitudes can be found: for small forcing and dissipation, the solution curve is the well-known bended resonance. The comparison between numerical results and theoretical predictions by a previously developed weakly nonlinear theory is successfully attempted.
The authors then extend the barotropic, weakly nonlinear theory to stationary Rossby waves forced by large-scale orography and dissipated by Ekman friction at the surface, in the framework of the quasigeostrophic model continuous in the vertical direction. The waves are superimposed on vertical profiles of zonal wind and stratification parameters taken from observations of the wintertime Northern Hemisphere circulation. In near-resonant conditions, the weakly nonlinear theory predicts multiple amplitude equilibration of the eddy field for a fixed vertical profile of the zonal wind. The authors discuss the energetics of the stationary waves and show that the form drag and Ekman dissipation can be made very small even if realistic values of the parameters are taken, at variance with the barotropic case.
This model is proposed as the theoretical base for such phenomena as atmospheric blocking, bimodality, and weather regimes.
Abstract
In a preceding paper the authors showed that planetary waves of very different amplitudes can be sustained on the same configuration of the zonal wind by asymptotically balancing the energy contributions related to Ekman dissipation and orographic drag. The basic physical mechanism considered, namely, nonlinear self-interaction of the eddy field, was modeled in a vertically continuous quasigeostrophic model by means of a perturbative approach that relies on an ad hoc choice of the meridional profile of the wave field itself. Given the mathematical limitations of this approach, some important aspects of the mechanism of resonance bending were not explored; in particular, the sensitivity of stationary solutions to changes in the zonal wind profile, channel geometry, and physical parameters such as dissipation coefficients and mountain height.
In the present paper, the robustness of the mechanism of resonance folding by numerical means is analyzed, in the framework of both the barotropic and the two-level quasigeostrophic model. It is demonstrated that resonance bending is a generic property of the equations governing atmospheric motions on the planetary scale. In particular, it is shown that multiple stationary solutions can be achieved with realistic values of Ekman dissipation and mountain height in the context of the two-level quasigeostrophic model.
The authors formulate a weakly nonlinear theory that does not rely on any a priori assumptions about the meridional structure of the solution. Numerical and analytical results are compared, obtaining a satisfactory agreement in the parameter range in which the asymptotic theory is valid. The authors conclude that the present model is still a good candidate for the explanation of one of the most relevant statistical property of low-frequency variability at midlatitudes, namely, that large amplitude fluctuations of ultralong waves correspond to small variations of the zonal wind.
Abstract
In a preceding paper the authors showed that planetary waves of very different amplitudes can be sustained on the same configuration of the zonal wind by asymptotically balancing the energy contributions related to Ekman dissipation and orographic drag. The basic physical mechanism considered, namely, nonlinear self-interaction of the eddy field, was modeled in a vertically continuous quasigeostrophic model by means of a perturbative approach that relies on an ad hoc choice of the meridional profile of the wave field itself. Given the mathematical limitations of this approach, some important aspects of the mechanism of resonance bending were not explored; in particular, the sensitivity of stationary solutions to changes in the zonal wind profile, channel geometry, and physical parameters such as dissipation coefficients and mountain height.
In the present paper, the robustness of the mechanism of resonance folding by numerical means is analyzed, in the framework of both the barotropic and the two-level quasigeostrophic model. It is demonstrated that resonance bending is a generic property of the equations governing atmospheric motions on the planetary scale. In particular, it is shown that multiple stationary solutions can be achieved with realistic values of Ekman dissipation and mountain height in the context of the two-level quasigeostrophic model.
The authors formulate a weakly nonlinear theory that does not rely on any a priori assumptions about the meridional structure of the solution. Numerical and analytical results are compared, obtaining a satisfactory agreement in the parameter range in which the asymptotic theory is valid. The authors conclude that the present model is still a good candidate for the explanation of one of the most relevant statistical property of low-frequency variability at midlatitudes, namely, that large amplitude fluctuations of ultralong waves correspond to small variations of the zonal wind.
Abstract
The response of a simple quasi-unidimensional barotropic model is studied. Wave-wave interaction, and bending the linear resonant response to the topographic forcing allows multiple equilibria if the zonal mean flow is assigned. The stationary solutions corresponding to the equilibria are compared with the observations.
Abstract
The response of a simple quasi-unidimensional barotropic model is studied. Wave-wave interaction, and bending the linear resonant response to the topographic forcing allows multiple equilibria if the zonal mean flow is assigned. The stationary solutions corresponding to the equilibria are compared with the observations.
