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A. Trevisan
and
A. Buzzi

Abstract

Stationary solutions and their stability properties of nondissipative barctropic flow in a narrow, longitudinally periodic channel on a βplane with a sheared basic current and bottom topography are investigated. An analytical treatment is applied which has been used in studies of solitary Rossby waves and is allowed by the choice of geometry. This leads to an ordinary nonlinear differential equation for the longitude-dependent part of the solution. The equation which is obtained in the present case is formally that of an anharmonic oscillator with external forcing and weakly variable natural frequency. Approximate analytical and numerical solutions are obtained under quasi-resonant conditions. Three possible states are found in a certain range of the parameters. Of these, only two are found to be stable. The implications of the existence of multiple solutions, also found by other authors in various contexts, for the large-scale atmospheric circulation and the phenomenon of blocking are discussed.

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A. Trevisan
and
U. Giostra

Abstract

The structure of the most unstable baroclinic mode in the presence of elongated topography oriented parallel to the basic state zonal current has been investigated in a number of studies. The topographic modification leads to enhanced baroclinic activity on the southern side of the mountain. The results found in simple quasi-geostrophic models with a ridge were generalized to primitive equations and realistically high and steep isolated topography; the same type of north–south asymmetry apt to explain lee cyclogenesis was observed.

In the present study we use a quasi-geostrophic two-layer model with a bottom ridge to investigate the dynamical balance leading to this type of asymmetry. In the case of a purely barotropic Rossby wave, we find that the topographic correction always leads to intensification of the undisturbed wave south of the mountain barrier. In the case of unstable baroclinic waves in the f-plane, a simple criterion holds that determines the conditions favoring lee cyclogenesis in terms of the basic state potential vorticity. The effect of β modifies the criterion and contributes to lee deepening.

The computation of the most unstable normal mode with a primitive equation model and a basic state derived from an Alpex lee cyclogenesis case further supports our findings concerning the robustness of the normal mode topographic correction in relation to the initial value problem and the basic state properties.

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A. Buzzi
,
A. Trevisan
, and
A. Speranza

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.

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P. Malguzzi
,
A. Trevisan
, and
A. Speranza

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.

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A. Speranza
,
A. Buzzi
,
A. Trevisan
, and
P. Malguzzi

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.

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A. Trevisan
,
L. Ferranti
, and
P. Malguzzi

Abstract

This work is an extension of the normal mode theory of lee cyclogenesis in that it removes all the simplifications and restrictive assumptions contained in previous formulations Linearized primitive equations in isentropic coordinates are integrated in time to find the most unstable eigenmode. The appropriate boundary condition for such a model applied either at z = 0 or z = h is derived. Results obtained in the β-plane with a realistically steep and high isolated topography are discussed in relation to the basic state characteristics. Limits and prospects with respect to theory verification are also discussed.

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