The evolution of the Arctic polar vortex during observed major midwinter stratospheric sudden warmings (SSWs) is investigated for the period 1957–2002, using 40-yr European Centre for Medium-Range Weather Forecasts (ECMWF) Re-Analysis (ERA-40) Ertel’s potential vorticity (PV) and temperature fields. Time-lag composites of vertically weighted PV, calculated relative to the SSW onset time, are derived for both vortex-displacement SSWs and vortex-splitting SSWs, by averaging over the 15 recorded displacement and 13 splitting events. The evolving vertical structure of the polar vortex during a typical SSW of each type is clearly illustrated by plotting an isosurface of the composite PV field, and is shown to be very close to that observed during representative individual events. Results are verified by comparison with an elliptical diagnostic vortex moment technique. For both types of SSW, little variation is found between individual events in the orientation of the developing vortex relative to the underlying topography; that is, the location of the vortex during SSWs of each type is largely fixed in relation to the earth’s surface. During each type of SSW, the vortex is found to have a distinctive vertical structure. Vortex-splitting events are typically barotropic, with the vortex split occurring near simultaneously over a large altitude range (20–40 km). In the majority of cases, of the two daughter vortices formed, it is the “Siberian” vortex that dominates over its “Canadian” counterpart. In contrast, displacement events are characterized by a very clear baroclinic structure; the vortex tilts significantly westward with height, so that the top and bottom of the vortex are separated by nearly 180° longitude before the upper vortex is sheared away and destroyed.

Back trajectories driven by large‐scale analyzed wind fields are used to investigate troposphere to stratosphere transport (TST) in the Northern Hemisphere tropopause region, as well as the surface sources for such transport, defined in terms of the locations where each trajectory last left the atmospheric boundary layer (log pressure height z* < 1 km). The proportion χBL of those trajectories arriving in the tropopause region that have visited the boundary layer within the previous fixed time period (typically 30 days) is determined as a function of each trajectory's final equivalent latitude and potential temperature. For a range of potential temperature surfaces (∼300–380 K), χBL is shown to have a sharp gradient in the extratropics indicative of a partial permeable barrier to transport that can be identified as a “Lagrangian tropopause.” Variations in χBL with equivalent latitude and potential temperature and on seasonal timescales are shown to provide a novel measure for the relative location and permeability of the tropopause barrier. Details such as the presence of a “ventilated layer” in the northern summer extratropical lower stratosphere (∼370–410 K) are clearly apparent. Directly below this layer (340–370 K) the tropopause barrier to transport is shown to be relatively strong, whereas below 340 K it is again more permeable. A distinction can therefore be made between “extratropical” TST that primarily ventilates the lowermost stratosphere below 340 K and “tropical” TST that occurs into the 370–410 K ventilated layer. The boundary layer source regions for extratropical TST are shown to correspond to those regions previously identified as sources for deep frontal uplift in the warm conveyor belt circulations of extratropical cyclones, although elevated regions such as the Himalayan plateau are also seen to be important. Tropical TST has different source regions associated with regions of active deep convection such as the western tropical Pacific and, in the northern summer, the Indian subcontinent. The source regions are, in general, found to be geographically localized, leading to the conclusion that subject to the limitations of the methodology, trace gas emissions in specific regions are substantially more likely to be transported to the lowermost stratosphere than elsewhere. The implications for the assessment of ozone depletion by very short lived halogenated species are mentioned.

The fundamental dynamics of ''vortex splitting'' stratospheric sudden warmings (SSWs), which are known to be predominantly barotropic in nature, are reexamined using an idealized single-layer f-plane model of the polar vortex. The aim is to elucidate the conditions under which a stationary topographic forcing causes the model vortex to split, and to express the splitting condition as a function of the model parameters determining the topography and circulation.For a specified topographic forcing profile the model behavior is governed by two nondimensional parameters: the topographic forcing height M and a surf-zone potential vorticity parameter V. For relatively low M, vortex splits similar to observed SSWs occur only for a narrow range of V values. Further, a bifurcation in parameter space is observed: a small change in V (or M) beyond a critical value can lead to an abrupt transition between a state with low-amplitude vortex Rossby waves and a sudden vortex split. The model behavior can be fully understood using two nonlinear analytical reductions: the Kida model of elliptical vortex motion in a uniform strain flow and a forced nonlinear oscillator equation. The abrupt transition in behavior is a feature of both reductions and corresponds to the onset of a nonlinear (self-tuning) resonance. The results add an important new aspect to the ''resonant excitation'' theory of SSWs. Under this paradigm, it is not necessary to invoke an anomalous tropospheric planetary wave source, or unusually favorable conditions for upward wave propagation, in order to explain the occurrence of SSWs. 1 The present study casts doubt on the accuracy of quasi-linear wave-mean models such as that used by Smith, as it is shown explicitly in section 4d that the interaction of weakly nonlinear vortex Rossby waves with their second harmonic is equally important as their interaction with the zonal mean flow.

Dam-break and lock-exchange flows are considered in a Boussinesq two-layer fluid system in a uniform two-dimensional channel. The focus is on inviscid 'weak' dam breaks or lock exchanges, for which waves generated from the initial conditions do not break, but instead disperse in a so-called undular bore. The evolution of such flows can be described by the Miyata-Camassa-Choi (MCC) equations. Insight into solutions of the MCC equations is provided by the canonical form of their long wave limit, the two-layer shallow water equations, which can be related to their single-layer counterpart via a surjective map. The nature of this surjective map illustrates that whilst some Riemann-type initial-value problems (dam breaks) are analogous to those in the single-layer problem, others (lock exchanges) are not. Previous descriptions of MCC waves of permanent form (cnoidal and solitary waves) are generalised, including a description of the effects of a regularising surface tension. The wave solutions allow the application of a technique due to El's approach, based on Whitham's modulation theory, which is used to determine key features of the expanding undular bore as a function of the initial conditions. A typical dam-break flow consists of a leftwardspropagating simple rarefaction wave and a rightward-propagating simple undular bore. The leading and trailing edge speeds, leading edge solitary wave amplitude and trailing edge linear wavelength are determined for the undular bore. Lock-exchange flows, for which the initial interface shape crosses the mid-depth of the channel, by contrast, are found to be more complex, and depending on the value of the surface tension parameter may include 'solibores' or fronts connecting two distinct regimes of long-wave behaviour. All of the results presented are informed and verified by numerical solutions of the MCC equations.

[1] The transport, mixing, and three-dimensional evolution of chemically distinct air masses within growing baroclinic waves are studied in idealized, high-resolution, life cycle experiments using suitably initialized passive tracers, contrasting the two well-known life cycle paradigms, distinguished by predominantly anticyclonic (LC1) or cyclonic (LC2) flow at upper levels. Stratosphere-troposphere exchange differs significantly between the two life cycles. Specifically, transport from the stratosphere into the troposphere is significantly larger for LC2 (typically by 50%), due to the presence of large and deep cyclonic vortices that create a wider surf zone than for LC1. In contrast, the transport of tropospheric air into the stratosphere is nearly identical between the two life cycles. The mass of boundary layer air uplifted into the free troposphere is similar for both life cycles, but much more is directly injected into the stratosphere in the case of LC1 (fourfold, approximately). However, the total mixing of boundary layer with stratospheric air is larger for LC2, owing to the presence of the deep cyclonic vortices that entrain and mix both boundary layer air from the surface and stratospheric air from the upper levels. For LC1, boundary layer and stratospheric air are brought together by smaller cyclonic structures that develop on the poleward side of the jet in the lower part of the middleworld, resulting in correspondingly weaker mixing. As both the El Niño-Southern Oscillation and the North Atlantic Oscillation are correlated with the relative frequency of life cycle behaviors, corresponding changes in chemical transport and mixing are to be expected.