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Abstract
The theory of cyclogenesis in the lee of the Alps presented by Speranza et al. in Part I is reexamined here (Part II) in the context of models dealing with finite amplitude topography. This generalization leads to the specification of the limits of validity of the approximations made in Part I and, at the same time, allows us to calculate the stability properties and normal mode structure of the model atmosphere with realistic topography. The effects of finite slope and finite geometrical height of the mountain are considered separately and their relative importance is evaluated. In the case of a three-dimensional obstacle with an idealized shape simulating the Alps, the modifications induced by the orography on the free, baroclinically unstable modes show essentially the same features observed in numerical experiments, including the orientation of the dipolar structure in the pressure perturbation across the mountain.
Abstract
The theory of cyclogenesis in the lee of the Alps presented by Speranza et al. in Part I is reexamined here (Part II) in the context of models dealing with finite amplitude topography. This generalization leads to the specification of the limits of validity of the approximations made in Part I and, at the same time, allows us to calculate the stability properties and normal mode structure of the model atmosphere with realistic topography. The effects of finite slope and finite geometrical height of the mountain are considered separately and their relative importance is evaluated. In the case of a three-dimensional obstacle with an idealized shape simulating the Alps, the modifications induced by the orography on the free, baroclinically unstable modes show essentially the same features observed in numerical experiments, including the orientation of the dipolar structure in the pressure perturbation across the mountain.
Abstract
Stationary flow of a barotropic fluid in a β channel has been shown by Charney and De Vore (1979) to possess multiple-equilibrium solutions when sinusoidal topographic forcing is exerted within the region of resonance near the wavenumber of stationary Rossby waves, and nonlinear effects are taken into account. Charney and De Vore associate the different solutions with zonal and blocking states of global circulation. However, real topography is non-sinusoidal and, most of the time, observed blocking configurations display a pronounced regional character. On the other hand, the problem of superimposing different harmonics is made difficult here by the essential role played by nonlinearity in the theory of multiple equilibria.
In this paper, the mathematical problem of determining the stationary states of flow of barotropic fluid in a β plane when topography is nonsinusoidal is analyzed with the help of the perturbative assumptions that the latitudinal scale of the flow is very large and topography has the form of a slowly modulated sinusoid.
The multiple states of stationary flow described by Charney and De Vore are found to exist simultaneously in different regions of the β plane. Theoretical solutions corresponding to different kinds of resonant forcing are analyzed.
The theoretical solutions are discussed in relationship to the problem of blocking as a “regional” phenomenon and are shown to have several different features in common with observed persistent blocking patterns.
Abstract
Stationary flow of a barotropic fluid in a β channel has been shown by Charney and De Vore (1979) to possess multiple-equilibrium solutions when sinusoidal topographic forcing is exerted within the region of resonance near the wavenumber of stationary Rossby waves, and nonlinear effects are taken into account. Charney and De Vore associate the different solutions with zonal and blocking states of global circulation. However, real topography is non-sinusoidal and, most of the time, observed blocking configurations display a pronounced regional character. On the other hand, the problem of superimposing different harmonics is made difficult here by the essential role played by nonlinearity in the theory of multiple equilibria.
In this paper, the mathematical problem of determining the stationary states of flow of barotropic fluid in a β plane when topography is nonsinusoidal is analyzed with the help of the perturbative assumptions that the latitudinal scale of the flow is very large and topography has the form of a slowly modulated sinusoid.
The multiple states of stationary flow described by Charney and De Vore are found to exist simultaneously in different regions of the β plane. Theoretical solutions corresponding to different kinds of resonant forcing are analyzed.
The theoretical solutions are discussed in relationship to the problem of blocking as a “regional” phenomenon and are shown to have several different features in common with observed persistent blocking patterns.
Abstract
The theory of the baroclinic instability of a nonsymmetric basic state in the presence of shallow sinusoidal topography is analyzed. The limiting case of vanishing topography (instability of a baroclinic Rossby wave) is also critically reexamined as far as some properties, potentially relevant for an explanation of the nonpropagating variance of the westerlies, are concerned.
Orographic instabilities modified by the nonhoinogeneity of the basic state are found. The unstable perturbations display properties that resemble those typical of the observed long-period variability of extratropical winter circulation in the Northern Hemisphere. Some possible physical implications of the existence of such instabilities in the context of the theory of the atmospheric circulation are suggested.
Abstract
The theory of the baroclinic instability of a nonsymmetric basic state in the presence of shallow sinusoidal topography is analyzed. The limiting case of vanishing topography (instability of a baroclinic Rossby wave) is also critically reexamined as far as some properties, potentially relevant for an explanation of the nonpropagating variance of the westerlies, are concerned.
Orographic instabilities modified by the nonhoinogeneity of the basic state are found. The unstable perturbations display properties that resemble those typical of the observed long-period variability of extratropical winter circulation in the Northern Hemisphere. Some possible physical implications of the existence of such instabilities in the context of the theory of the atmospheric circulation are suggested.
Abstract
A semilinear (the wave-dynamics are linear with the time-evolution operator determined by the time-varying zonal flow while the zonal flow is fully nonlinear in the eddy fluxes) model of a baroclinic zonal jet is integrated, under macroscopic conditions realistic for the earth's atmosphere, for a time period of 20 years in a high resolution pseudospectral version and its asymptotic (in time) statistical properties are determined.
The model is studied as a dynamical system, both by following sequences of bifurcations from the stable. Hadley circulation and by embedding in lower dimension spaces. The model turns out to be far from amenable to weakly nonlinear approximations common in atmospheric and oceanographic literature.
The analysis of propagation of disturbances in the turbulent jet demonstrates the inadequacy of mean-field approximations usually adopted in studies of kinematics of Rossby waves, teleconnections, etc.
Abstract
A semilinear (the wave-dynamics are linear with the time-evolution operator determined by the time-varying zonal flow while the zonal flow is fully nonlinear in the eddy fluxes) model of a baroclinic zonal jet is integrated, under macroscopic conditions realistic for the earth's atmosphere, for a time period of 20 years in a high resolution pseudospectral version and its asymptotic (in time) statistical properties are determined.
The model is studied as a dynamical system, both by following sequences of bifurcations from the stable. Hadley circulation and by embedding in lower dimension spaces. The model turns out to be far from amenable to weakly nonlinear approximations common in atmospheric and oceanographic literature.
The analysis of propagation of disturbances in the turbulent jet demonstrates the inadequacy of mean-field approximations usually adopted in studies of kinematics of Rossby waves, teleconnections, etc.
Abstract
We discuss some statistical properties of the observed tropospheric circulation in Northern Hemisphere mid-latitudes. The data used consist of the twice-daily 500 mb height NMC analyses for the period 1966–77. Our analysis is performed in the context of the quasi-unidimensional theory. Estimates of the probability distribution of wave amplitude in the low-frequency range (10–40 days) seem to reveal a bimodal character, while similar estimates for the zonal wind fail to show stable multiple peaks in the occupation frequency, although the process involved seems to be more complex than Gaussian. Possible dynamical interpretations of such statistical properties are discussed in the light of other properties resulting from different types of analysis. The emerging physical picture reveals an intermittent process, operating on planetary scales through a predominantly baroclinic conversion, in agreement with the theoretical considerations of Benzi et al.
Abstract
We discuss some statistical properties of the observed tropospheric circulation in Northern Hemisphere mid-latitudes. The data used consist of the twice-daily 500 mb height NMC analyses for the period 1966–77. Our analysis is performed in the context of the quasi-unidimensional theory. Estimates of the probability distribution of wave amplitude in the low-frequency range (10–40 days) seem to reveal a bimodal character, while similar estimates for the zonal wind fail to show stable multiple peaks in the occupation frequency, although the process involved seems to be more complex than Gaussian. Possible dynamical interpretations of such statistical properties are discussed in the light of other properties resulting from different types of analysis. The emerging physical picture reveals an intermittent process, operating on planetary scales through a predominantly baroclinic conversion, in agreement with the theoretical considerations of Benzi et al.
Abstract
The presence of bottom topography in a baroclinic flow modifies the properties of the propagating baroclinic unstable modes and allows for the appearance of new unstable modes which are nonpropagating, as first shown by Charney and Straus. Mountain form-drag, which provides a coupling mechanism between the zonal flow and the waves, is the essential ingredient for topographic instability. In this paper, the properties of instability for both zonally symmetric and asymmetric baroclinic basic states in the presence of topographic forcing are investigated. The results in a two-layer and a continuously stratified atmosphere are also compared and discussed. We find that two different types of topographic instability exist, one which is essentially baroclinic and is present in symmetric and asymmetric basic states, the other which is mixed barotropic-baroclinic and is present only in asymmetric basic states.
Abstract
The presence of bottom topography in a baroclinic flow modifies the properties of the propagating baroclinic unstable modes and allows for the appearance of new unstable modes which are nonpropagating, as first shown by Charney and Straus. Mountain form-drag, which provides a coupling mechanism between the zonal flow and the waves, is the essential ingredient for topographic instability. In this paper, the properties of instability for both zonally symmetric and asymmetric baroclinic basic states in the presence of topographic forcing are investigated. The results in a two-layer and a continuously stratified atmosphere are also compared and discussed. We find that two different types of topographic instability exist, one which is essentially baroclinic and is present in symmetric and asymmetric basic states, the other which is mixed barotropic-baroclinic and is present only in asymmetric basic states.
Abstract
Baroclinic instability in the presence of steep finite amplitude topography is studied in the primitive equation model. The quasi-geostrophic theory of Alpine cyclogenesis of Speranza et al. is reanalyzed and discussed in this context.
The present model is a generalization of the one used by Stone to include topographic effects, lateral shear of the basic wind, and/or lateral walls. We focus in particular on the differences between this formulation and the quasi-geostrophic one when the meridional scale of the topography is very small (of the order of 100 km). We find that only in the primitive equation model does a small-volume mountain, of height and width comparable with those of the Alps, introduce significant large-scale modifications to the baroclinic modes. The most unstable mode attains its maximum amplitude to the southern side of the mountain. We show that these results do not depend upon the specification of the lateral boundary conditions provided the basic state baroclinicity is meridionally confined.
Abstract
Baroclinic instability in the presence of steep finite amplitude topography is studied in the primitive equation model. The quasi-geostrophic theory of Alpine cyclogenesis of Speranza et al. is reanalyzed and discussed in this context.
The present model is a generalization of the one used by Stone to include topographic effects, lateral shear of the basic wind, and/or lateral walls. We focus in particular on the differences between this formulation and the quasi-geostrophic one when the meridional scale of the topography is very small (of the order of 100 km). We find that only in the primitive equation model does a small-volume mountain, of height and width comparable with those of the Alps, introduce significant large-scale modifications to the baroclinic modes. The most unstable mode attains its maximum amplitude to the southern side of the mountain. We show that these results do not depend upon the specification of the lateral boundary conditions provided the basic state baroclinicity is meridionally confined.
Abstract
A recent analysis of atmospheric observations has shown evidence of bimodality in the statistical distribution of wave amplitude in the ultralong (zonal wavenumber group 2–4), low frequency (period >5 days). Similar analysis of the zonal wind and its average shear shows no clear sign of bimodality. Both are characterized by a very variance (≅ 1 m s−1) and the associated kinetic energy fluctuations are not sufficient to account for the variations in wave amplitudes. Global energetic analysis confirms this finding. maintenance of the waves is dominated by baroclinic processes. On the other hand, from a theoretical point of view, barotropic models for wave generation and maintenance be brought into agreement with observed statistics by introducing nonlinear bending of the stationary resonant response to topographic modulation allowing different values of the equilibrium amplitude to correspond to the same value of the zonal flow. However, because of aforementioned energetic difficulties, in a barotropic model the closure equation (form-drag) for the zonal flow does not select states corresponding to values of the zonal wind within the observed statistics for any realistic value of the external parameters (dissipation and momentum forcing). In this paper we show how the inclusion wave field self interaction produces resonance bending in a minimal baroclinic model. The two resulting equilibrium stable states can be achieved within a realistic range of the zonal flow. Moreover, the equilibrium states are characterized by stability properties which, on a theoretical level, are much more satisfactory than in the linear resonance.
Abstract
A recent analysis of atmospheric observations has shown evidence of bimodality in the statistical distribution of wave amplitude in the ultralong (zonal wavenumber group 2–4), low frequency (period >5 days). Similar analysis of the zonal wind and its average shear shows no clear sign of bimodality. Both are characterized by a very variance (≅ 1 m s−1) and the associated kinetic energy fluctuations are not sufficient to account for the variations in wave amplitudes. Global energetic analysis confirms this finding. maintenance of the waves is dominated by baroclinic processes. On the other hand, from a theoretical point of view, barotropic models for wave generation and maintenance be brought into agreement with observed statistics by introducing nonlinear bending of the stationary resonant response to topographic modulation allowing different values of the equilibrium amplitude to correspond to the same value of the zonal flow. However, because of aforementioned energetic difficulties, in a barotropic model the closure equation (form-drag) for the zonal flow does not select states corresponding to values of the zonal wind within the observed statistics for any realistic value of the external parameters (dissipation and momentum forcing). In this paper we show how the inclusion wave field self interaction produces resonance bending in a minimal baroclinic model. The two resulting equilibrium stable states can be achieved within a realistic range of the zonal flow. Moreover, the equilibrium states are characterized by stability properties which, on a theoretical level, are much more satisfactory than in the linear resonance.
Abstract
Observational and numerical studies on Alpine cyclogenesis have shown that a developing baroclinic wave approaching the mountain region gives rise to a disturbance of dipolar structure, extending throughout the troposphere with horizontal scales comparable to the Rossby deformation radius. It is possible to interpret such disturbances as modifications of baroclinically unstable modes, induced by localized topography.
In the present approach, the effect of the mountain is introduced in a perturbative sense, in the framework of quasi-geostrophic theory. Even in this simple approach the spatial structure of the unstable modes is modified by a localized topography in the direction required in order to explain the observed features. In the case of a continuously stratified fluid, the basic characteristics of the observed vertical structure are also reproduced.
Abstract
Observational and numerical studies on Alpine cyclogenesis have shown that a developing baroclinic wave approaching the mountain region gives rise to a disturbance of dipolar structure, extending throughout the troposphere with horizontal scales comparable to the Rossby deformation radius. It is possible to interpret such disturbances as modifications of baroclinically unstable modes, induced by localized topography.
In the present approach, the effect of the mountain is introduced in a perturbative sense, in the framework of quasi-geostrophic theory. Even in this simple approach the spatial structure of the unstable modes is modified by a localized topography in the direction required in order to explain the observed features. In the case of a continuously stratified fluid, the basic characteristics of the observed vertical structure are also reproduced.
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.
