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Carlos R. Mechoso and Douglas M. Sinton

Abstract

The energy analysis of the two-layer frontal model of Kotchin (1932) and Orlanski (1968) is reformulated. The new formulation is based on separating the contributions to the eddy kinetic energy of the unstable waves by the changes in 1) the difference in relative momentum between the layers (multiplied by the shear), and in 2) the available potential energy. Such a separation results in a clear characterization of the instabilities, particularly near the Rayleigh, Helmholtz and baroclinic instability limits. The mean meridional circulation induced by the unstable waves is analyzed.

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Douglas M. Sinton and William D. Heise

Abstract

A two-layer frontal model is adapted to investigate the stability of fronts in the presence of potential vorticity (PV) anomalies corresponding to cross-front shear of the mean alongfront flow. Introducing shear modifies the unstable baroclinic modes that exist in the original unsheared model. In addition, the shear produces two new unstable ageostrophic modes. One of these new modes is characterized by barotropic instability, while the other is a shallow mode characterized by a mixed barotropic–baroclinic instability. The alongfront scale of the most unstable mode in both cases is determined by the scale of the anomaly.

The barotropic mode requires some PV anomaly in both layers, whereas the mixed mode can exist with an anomaly confined to the lower layer only. The maximum growth rate of the barotropic mode is independent of the scale of the PV anomaly and the Richardson number of the flow. Anomalies in the basic-state relative vorticity of 10−4 s−1 produce growth rates of 1.45 day−1. The mixed mode is moderately destabilized for anomalies on the scale of the Rossby radius of deformation with a maximum growth rate of 1 day−1.

A baroclinic frontal mode that exists for the unsheared case has its growth rate tripled to 1.82 day−1 when a mean vorticity anomaly of 10−4 s−1 is introduced on the scale of the Rossby radius of deformation. This has implications for rapid cyclogenesis.

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Douglas M. Sinton and Carlos R. Mechoso

Abstract

A two-layer, shallow-water frontal model on an f-plane is used to study the nonlinear evolution of frontal waves. The fluid is confined to a periodic channel with parallel vertical walls. It is found that, at an advanced stage in the evolution of frontal waves, small-scale disturbances develop along the cold front while the warm front evolves in a smooth fashion. It is shown that the motion field associated with the primary low advects kinetic energy and low potential vorticity into the cold-frontal region. That kinetic energy is transferred by barotropic processes to the secondary disturbances at locations along the cold front where advection of low potential vorticity results in an enhancement of the horizontal shears. On the other hand, kinetic energy is removed from the warm-frontal region, which remains undisturbed.

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Carlos R. Mechoso and Douglas M. Sinton

Abstract

The stability of baroclinic flows with horizontal shear over sloping topography is analyzed with special emphasis on the structure and energetics of the unstable perturbatiorts. The study is conducted by using a linearized two-layer quasi-geostrophic channel model for different topography profiles and distributions of the basic velocity field. Interactions between the two fluid layers and the energy conversions by the unstable porturbations are described. It is found that topography sloping as (opposed to) the fluid interface contributes to enhance the perturbation amplitude in the upper (lower) layer relative to the lower (upper) layer. The results for bottom topography with dithering characteristics across the flow indicate pronounced localized effects on the energy conversions over the slopes and the meridional scale of the perturbations in the lower layer.

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Brian H. Kahn and Douglas M. Sinton

Abstract

The existence, scale, and growth rates of subsynoptic-scale warm-core circulations are investigated with a simple parameterization for latent heat release in a nonconvective basic state using a linear two-layer shallow-water model. For a range of baroclinic flows from moderate to high Richardson number, conditionally stable lapse rates approaching saturated adiabats consistently yield the most unstable modes with a warm-core structure and a Rossby number ∼O(1), with higher Rossby numbers stabilized. This compares to the corresponding most unstable modes for the dry cases that have cold-core structures and Rossby numbers ∼O(10−1) or in the quasigeostrophic range. The maximum growth rates of 0.45 of the Coriolis parameter are an order of magnitude greater than those for the corresponding most unstable dry modes. Because the Rossby number of the most unstable mode for nearly saturated conditions is virtually independent of Richardson number, the preferred scale of these warm-core modes varies directly with the mean vertical shear for a given static stability.

This scale relation suggests that the requirement to maintain nearly saturated conditions on horizontal scales sufficient for development can be met more easily on the preferred subsynoptic horizontal scales associated with weak vertical shear. Conversely, the lack of instability for higher Rossby numbers implies that stronger vertical shears stabilize smaller subsynoptic regions that are destabilized for weaker vertical shears. This has implications for the scale and existence of warm-core circulations in the tropics, such as those assumed a priori in wind-induced surface heat exchange (WISHE).

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