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Martin Juckes

Abstract

The dynamical properties of potential temperature anomalies on the tropopause are analyzed for quasigeo-strophic flow on an f plane. The potential vorticity is taken to he piecewise constant, with a single discontinuity at the tropopause. The tropopause potential temperature, on scales too small to feel the lower boundary, is found to be proportional to the tropopause geopotential height. The constant of proportionality is the geometric mean of the stratospheric and tropospheric lapse rates. Results from a general circulation model are found to be in agreement with this prediction.

The streamfunction associated with a combination of anomalies on the lower boundary and tropopause is also derived. The solution, determined completely by the potential temperature distributions, in general has a nonzero velocity at the lower boundary. Applying the theory to the time-mean zonal-mean jets, which must have a near-zero velocity at the ground, imposes a constraint on parameters defining the jet.

The dynamical properties of the system are further elucidated using the scaling argument previously applied by Charney to geostrophic turbulence. Charney's assumption of vertical homogeneity is replaced by the assumption that the dynamics is concentrated around the tropopause. In the nonlinear cascade to small scales the Rossby number is predicted to increase with horizontal wavenumber, leading to an eventual breakdown of geostrophic balance.

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Martin Juckes

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Martin Juckes

Abstract

The structure of idealized two-dimensional shear lines has been calculated for specified tropopause potential temperature anomalies. A cold anomaly corresponds to an intrusion of stratospheric air into the troposphere. A balanced hydrostatic primitive equation structure is derived using an iterative technique. The resulting wind and vertical displacement of the tropopause are compared with a recent result extending quasigeostrophic theory to situations where the variation of potential vorticity along an isentrope or isobar is large, as is the case, for instance, when the isosurface intersects the tropopause. The formulation of the theory is clarified by analyzing the relation between quasigeostrophic potential vorticity and Ertel’s potential vorticity. The comparison between the low–Rossby number theoretical approximation and primitive equation structures confirms the theoretical prediction that the relative error is proportional to the Rossby number. The constant of proportionality is close to unity. The effect of the lower boundary condition on the shear line structure is analyzed. For a shear line consisting of an upper-tropospheric potential vorticity anomaly in the absence of a surface temperature anomaly it is found that the horizontal extent of the wind is not limited, as might have been expected, by the Rossby deformation radius, but rather by the largest scale of the shear line, which may be somewhat greater.

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Martin Juckes

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The shallow water equations are used to investigate the interaction of planetary wave-breaking with a “diabatic” forcing. The numerical integrations demonstrate the formation of a sharp gradient in potential vorticity at the edge of the polar vortex, despite “diabatic relaxation” towards a smooth gradient. Successive cycles of Rossby wave-breaking accentuate the distinction between the vortex and the surf-zone. Persistent easterly acceleration in the tropics eventually produces a flow regime of little relevance to the atmosphere. For the period when the flow has some qualitative resemblance to the middle stratosphere diffusion coefficients are calculated from the meridional fluxes of potential vorticity and of passive tracers. It is found that the unique dynamical nature of potential vorticity among tracers is not reflected in its diffusion coefficient.

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Martin Juckes

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An analytic linear stability analysis is carried out for a shear line associated with a surface temperature anomaly in uniform potential vorticity, quasigeostrophic flow. Previous studies of this type of flow, albeit with more realistic basic states, have relied on numerical solution. The instability can be interpreted as the result of the interaction of counterpropagating edge waves on the two opposing potential temperature gradients that bound the shear line.

The analytic normal mode analysis can easily be extended to investigate nonmodal disturbances. The disturbances defined by maximizing the growth of selected norms over the norms over the normal mode e-folding time generally show similar growth rates to the normal modes. There is weaker scale selectivity and a shift to longer wave-lengths. The enstrophy norm provides an exception to this behavior. This norm is sensitive to small-scale structures and can grow much faster than the large-scale disturbance.

Nonlinear integrations show the instability breaking the shear line into a string of vortices. Narrow secondary shear lines are formed with vorticity values much larger than those of the original shear line. These secondary shear lines are in turn broken up by the same instability mechanism.

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Leonhard Scheck, Sarah C. Jones, and Martin Juckes

Abstract

The influence of frontal waves on the interaction of a tropical cyclone and a tropopause front is investigated in an idealized framework. In a nondivergent barotropic model the front is represented by a vorticity step with a superimposed sinusoidal perturbation. This gives rise to a jet that meanders to the north and south and can be viewed as a sequence of upper-level troughs and ridges. The model evolution depends sensitively on the position of the cyclone relative to the troughs and ridges. Here a bifurcation point is identified that is located on the trough axis at a distance where the zonal speed of the background flow equals the phase speed of the wave. Arbitrarily small displacements from this position determine whether a cyclone is advected toward the front or repelled. Only a limited range of wavelengths can lead to track bifurcations. The largest effects are obtained for resonant frontal waves propagating with a phase speed matching the initial zonal translation speed of the cyclone. Weak and large-scale vortices can be disrupted when approaching the bifurcation point, where they are exposed to continuously strong shear deformation.

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Volkmar Wirth, Christof Appenzeller, and Martin Juckes

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The quasi-horizontal roll-up of unstable stratospheric intrusions into isolated vortices is known to result in specific structures on satellite water vapor images that are characterized by intermingling dark and light filaments. The current paper investigates how these features are generated and how they relate to partly similar features found on concurrent maps of the tropopause height or potential vorticity (PV). The roll-up of a stratospheric intrusion is simulated numerically with an idealized quasigeostrophic model, which focuses on the dynamics induced by anomalies in the height of the tropopause. The upper-tropospheric adiabatic vertical wind is calculated explicitly and is used to simulate water vapor images in the model. These images show qualitatively the same characteristic features as observed. They are generated through a combination of horizontal advection of initial moisture anomalies and the creation of additional moisture anomalies resulting from the upper-tropospheric vertical air motion. The latter is, in turn, induced by the quasi-horizontal motion of the tropopause anomaly. It is suggested that a substantial portion of the spiral-like structures on the water vapor images is likely to reflect the vertical wind induced by the evolution of the intrusion itself. When the tropopause is defined through a fairly low value of PV, it may acquire similar spiraling structures, as it is being advected almost like a passive tracer. On the other hand, for the dynamically active core part of the intrusion, which is located at higher values of PV, one may expect an evolution leading to more compact vortex cores and less structure overall.

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Leonhard Scheck, Sarah C. Jones, and Martin Juckes

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The interaction of a tropical cyclone and a zonally aligned tropopause front is investigated in an idealized framework. A nondivergent barotropic model is used in which the front is represented by a vorticity step, giving a jetlike velocity profile. The excitation of frontal waves by a cyclone located south of the front and the impact of the wave flow on the cyclone motion is studied for different representations of the cyclone and the jet. The evolution from the initial wave excitation until after the cyclone has crossed the front is discussed. The interaction becomes stronger with increasing jet speed. For cyclone representations containing negative relative vorticity, anticyclones develop and can influence the excitation of frontal waves significantly. Resonant frontal waves propagating with a phase speed matching the zonal translation speed of the cyclone are decisive for the interaction. The frontal wave spectrum excited by a cyclone on the front is dominated by waves that are in resonance in the initial phase. These waves have the largest impact on the cyclone motion.

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Juliane Otto, Calum Brown, Carlo Buontempo, Francisco Doblas-Reyes, Daniela Jacob, Martin Juckes, Elke Keup-Thiel, Blaz Kurnik, Jörg Schulz, Andrea Taylor, Tijl Verhoelst, and Peter Walton
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