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Volkmar Wirth

Abstract

This paper investigates stationary axisymmetric balanced flow of a stably stratified dry non-Boussinesq atmosphere on the f plane. The circulation is forced in the troposphere through thermal relaxation toward a specified equilibrium temperature and is damped through Rayleigh friction in the interior of the domain. Surface friction is sufficiently strong to ensure weak surface winds. As in the analogous zonally symmetric problem studied by Plumb and Hou there is threshold behavior in the frictionless limit with a thermal equilibrium solution for subcritical forcing and a highly nonlinear so-called angular momentum conserving (AMC) solution for supercritical forcing. The latter is characterized by a sharp outward edge of the vortex circulation and a nonvanishing secondary cross-vortex circulation. In the frictionless limit, the secondary circulation does not reach above the region of the thermal forcing. Noticeable differences of the current problem with respect to the zonally symmetric problem arise from the strong nonlinearity of the thermal wind equation and the nonzero thermal forcing right on the axis of symmetry. For the highly nonlinear AMC solution an approximate analytical theory is presented and verified by use of a numerical Eliassen balanced vortex model. This model is also used to investigate the nonlinear dependence of the secondary circulation on the Rayleigh friction coefficient and the penetration of the secondary circulation above the tropopause. An analytic Green’s function solution for the linearized problem gives insight into nonlinear asymptotic dependences. Thinking in terms of an Eliassen balanced vortex model offers a new view on the secondary circulation in the AMC regime.

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Volkmar Wirth

Abstract

No abstract available.

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Volkmar Wirth

Abstract

Idealized axisymmetric anomalies of potential vorticity (PV) on a midlatitude f plane and their related response in terms of balanced wind and temperature are investigated with special focus on the static stability in the tropopause region. The PV anomalies are specified such that they can be interpreted as the result of conservative advection in the tropopause region across the gradients of a prescribed background atmosphere with piecewise constant buoyancy frequency squared N 2. Related cyclones and anticyclones are treated identically except for the sign of the tropopause potential temperature anomaly. Composite profiles of N 2 are computed, for which the thermal tropopause is used as a common reference level and where the number of cyclones in the composite equals the number of anticyclones. One obtains a pronounced peak of N 2 just above the tropopause and slightly enhanced values below the tropopause in comparison with the background profile. Within the framework of PV inversion various mechanisms are identified. Important contributions to the peak in N 2 are due to the pronounced cyclone–anticyclone asymmetry in the vertical structure of the tangential wind, and to the poleward advection of high values of PV from the subtropical lower stratosphere. Qualitatively, the key features of the composite profiles are in good agreement with observations above southern Germany that have recently been compiled.

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Volkmar Wirth

Abstract

The differences between upper-tropospheric cyclones and anticyclones are investigated regarding the height of the thermal and the dynamical tropopause. The problem is addressed in an idealized framework by analyzing axisymmetric balanced flows, which are characterized by a radial scale ΔR and a tropopause potential temperature anomaly Δθ, where cyclones and anticyclones differ only by the sign of Δθ. The height of the thermal tropopause significantly differs from the height of the dynamical tropopause unless the anomaly is shallow. There is a pronounced asymmetry in that the differences are much larger and more likely to occur in the case of cyclones. Two factors contribute to this asymmetry. First, for a given amplitude |Δθ|, cyclones and anticyclones have different aspect ratios in geometric space; second, for a high-latitude winter scenario the critical lapse rate of the WMO thermal tropopause is asymmetric with respect to typical tropospheric and stratospheric lapse rates. Simulated station statistics regarding the height of the two tropopauses share essential qualitative features with similar statistics from observations. The asymmetry in the model sensitively depends on the lower-stratospheric lapse rate. Multiple tropopauses may greatly enhance the asymmetry.

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Volkmar Wirth

Abstract

Stationary planetary waves in the southern stratosphere display a characteristic seasonal cycle. Previous research based on a one-dimensional model suggests that this behavior is mainly determined by seasonally varying transmission properties of the atmosphere with respect to wave propagation. The issue is investigated with the help of a hemispheric, linear, quasi-geostrophic model. It reproduces well some of the observed qualitative features and is internally consistent in the sense that its seasonal wave cycle can be explained in terms of varying wave transmission properties of the mean circulation. On the other hand, the model does not yield the observed seasonal cycle. Despite considerable sensitivity to modifications in the basic-state wind and dissipation parameterization, the model could not be reasonably fit to reproduce the observed seasonal cycle. Possible reasons for the model deficiency are put forward. In summary, even though suggestive, the present study is not entirely conclusive about the degree to which the observed cycle is determined by wave transmission properties alone.

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Isabelle Prestel and Volkmar Wirth

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Banner clouds are clouds that are attached to the leeward slope of a steep mountain. Their formation is essentially due to strong Lagrangian uplift of air in the lee of the mountain. However, little is known about the flow regime in which banner clouds can be expected to occur. The present study addresses this question through numerical simulations of flow past idealized orography. Systematic sets of simulations are carried out exploring the parameter space spanned by two dimensionless numbers, which represent the aspect ratio of the mountain and the stratification of the flow. The simulations include both two-dimensional flow past two-dimensional orography and three-dimensional flow past three-dimensional orography.

Regarding flow separation from the surface, both the two- and the three-dimensional simulations show the characteristic regime behavior that has previously been found in laboratory experiments for two-dimensional orography. Flow separation is observed in two of the three regimes, namely in the “leeside separation regime,” which occurs preferably for steep mountains in weakly stratified flow, and in the “postwave separation regime,” which requires increased stratification. The physical mechanism for the former is boundary layer friction, while the latter may also occur for inviscid flow. However, flow separation is only a necessary, not sufficient condition for banner cloud formation. The vertical uplift and its leeward–windward asymmetry show that banner clouds cannot form in the two-dimensional simulations. In addition, even in the three-dimensional simulations they can only be expected in a small part of the parameter space corresponding to steep three-dimensional orography in weakly stratified flow.

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Georgios Fragkoulidis and Volkmar Wirth

Abstract

Transient Rossby wave packets (RWPs) are a prominent feature of the synoptic to planetary upper-tropospheric flow at the midlatitudes. Their demonstrated role in various aspects of weather and climate prompts the investigation of characteristic properties like their amplitude, phase speed, and group velocity. Traditional frameworks for the diagnosis of the two latter have so far remained nonlocal in space or time, thus preventing a detailed view on the spatiotemporal evolution of RWPs. The present work proposes a method for the diagnosis of horizontal Rossby wave phase speed and group velocity locally in space and time. The approach is based on the analytic signal of upper-tropospheric meridional wind velocity and RWP amplitude, respectively. The new diagnostics are first applied to illustrative examples from a barotropic model simulation and the real atmosphere. The main seasonal and interregional variability features of RWP amplitude, phase speed, and group velocity are then explored using ERA5 reanalysis data for the time period 1979–2018. Apparent differences and similarities in these respects between the Northern and Southern Hemispheres are also discussed. Finally, the role of RWP amplitude and phase speed during central European short-lived and persistent temperature extremes is investigated based on changes of their distribution compared to the climatology of the region. The proposed diagnostics offer insight into the spatiotemporal variability of RWP properties and allow the evaluation of their implications at low computational demands.

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Sebastian Schappert and Volkmar Wirth

Abstract

Banner clouds are clouds in the lee of steep mountains or sharp ridges. Previous work suggests that the main formation mechanism is vertical uplift in the lee of the mountain. On the other hand, little is known about the Lagrangian behavior of air parcels as they pass the mountain, which motivates the current investigation. Three different diagnostics are applied in the framework of large-eddy simulations of airflow past an isolated pyramid-shaped obstacle: Eulerian tracers indicating the initial positions of the parcels, streamlines along the time-averaged wind field, and online trajectories computed from the instantaneous wind field.

All three methods diagnose a plume of large vertical uplift in the immediate lee of the mountain. According to the time-mean Eulerian tracers, the cloudy parcels originated within a fairly small coherent area at the inflow boundary. In contrast, the time-mean streamlines indicate a bifurcation into two distinct classes of air parcels with very different characteristics. The parcels in the first class originate at intermediate altitudes, pass the obstacle close to its summit, and proceed directly into the cloud. By contrast, the parcels in the second class start at low altitude and take a fairly long time before they reach the cloud on a spiraling path. A humidity tracer quantifies mixing, revealing partial moistening for the first class of parcels and drying for the second class of parcels. For the online trajectories, the originating location of parcels is more scattered, but the results are still consistent with the basic features revealed by the other two diagnostics.

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Andreas Müller and Volkmar Wirth

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This note investigates the dependence of the extratropical tropopause inversion layer (TIL) on numerical resolution in an idealized modeling framework. Axisymmetric upper-tropospheric anticyclones are constructed by specifying potential vorticity (PV) and solving the nonlinear PV-inversion problem. The PV distribution has a smooth but near-discontinuous change of PV across the tropopause in a transition zone with vertical depth δ. For fixed δ the strength of the TIL changes with changing resolution until the transition zone is resolved by a fairly large number of grid points. The quality-controlled numerical solutions are used to study the behavior for δ → 0. This limit can lead to very strong TILs, but no indications for divergent behavior were found.

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Matthias Voigt and Volkmar Wirth

Abstract

Banner clouds are clouds in the lee of steep mountains or sharp ridges. Their formation has previously been hypothesized as due to three different mechanisms: (i) vertical uplift in a lee vortex (which has a horizontal axis), (ii) adiabatic expansion along quasi-horizontal trajectories (the so-called Bernoulli effect), and (iii) a mixing cloud (i.e., condensation through mixing of two unsaturated air masses).

In the present work, these hypotheses are tested and quantitatively evaluated against each other by means of large-eddy simulation. The model setup is chosen such as to represent idealized but prototypical conditions for banner cloud formation. In this setup the lee-vortex mechanism is clearly the dominant mechanism for banner cloud formation. An essential aspect is the pronounced windward–leeward asymmetry in the Lagrangian vertical uplift with a plume of large positive values in the immediate lee of the mountain; this allows the region in the lee to tap moister air from closer to the surface. By comparison, the horizontal pressure perturbation is more than two orders of magnitude smaller than the pressure drop along a trajectory in the rising branch of the lee vortex; the “Bernoulli mechanism” is, therefore, very unlikely to be a primary mechanism. Banner clouds are unlikely to be “mixing clouds” in the strict sense of their definition. However, turbulent mixing may lead to small but nonnegligible moistening of parcels along time-mean trajectories; although not of primary importance, the latter may be considered as a modifying factor to existing banner clouds.

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