A simple, dynamically consistent model of mixing and transport in Rossby-wave critical layers is obtained from the well-known Stewartson–Warn–Warn (SWW) solution of Rossby-wave critical-layer theory. The SWW solution is thought to be a useful conceptual model of Rossby-wave breaking in the stratosphere. Chaotic advection in the model is a consequence of the interaction between a stationary and a transient Rossby wave. Mixing and transport are characterized separately with a number of quantitative diagnostics (e.g. mean-square dispersion, lobe dynamics, and spectral moments), and with particular emphasis on the dynamics of the tracer field itself. The parameter dependences of the diagnostics are examined: transport tends to increase monotonically with increasing perturbation amplitude whereas mixing does not. The robustness of the results is investigated by stochastically perturbing the transient-wave phase speed. The two-wave chaotic advection model is contrasted with a stochastic single-wave model. It is shown that the effects of chaotic advection cannot be captured by stochasticity alone.

A new humidity analysis variable has been successfully introduced into the Met Office's variational data assimilation system. The new variable uses a transformation consisting of a nonlinear normalization and a link with temperature increments that is a function of background (forecast) humidity. The normalization (which is the more important aspect) makes the new variable's errors more symmetrical and thus better represented by the variational cost function. As in the previous operational system, water vapour and cloud are combined into a single total water variable for the analysis step. The transform is now operational in both global and limited‐area systems. The forecast improvements—to the mass as well as the humidity fields—are largest in the Southern Hemisphere and there is a better fit of both background and analysis to humidity‐sensitive satellite channels. The results suggest that the transformation is particularly beneficial for the use of satellite data. The transform reduces the problem of negative humidities in the analysis which were more prevalent over the ocean.

The residence time measures the rate at which a pollutant escapes from a region of interest. Previous studies of urban ventilation have estimated the mean residence time from Eulerian data by assuming a spatially homogeneous pollutant field. Using a large-eddy simulation and a Lagrangian particle model, the residence and exposure times are calculated for an idealized street canyon in the skimming-flow region and a deep street canyon within a realistic urban area. For both domains, the mean residence time is on the order of a canyon circulation time scale, while the mean exposure time, which includes re-entrainment and characterizes the total time spent by a pollutant in a region of interest, is about 20% longer. Intensive quantities such as the Lagrangian visitation factor and return coefficient indicate that re-entrainment is modest. Probability distribution functions of the exposure and residence times are nearly exponential for both domains, in accord with pure diffusion and single-time-scale, vertical-exchange parameterizations. It is argued that, by analogy with Brownian motion, the mean residence and exposure times are set primarily by the mean circulation rather than the turbulence when the flow approximates that within a two-dimensional street canyon.

The relevance of chaotic advection to stratospheric mixing and transport is addressed in the context of (i) a numerical model of forced shallow-water flow on the sphere, and (ii) a middle-atmosphere general circulation model. It is argued that chaotic advection applies to both these models if there is suitable large-scale spatial structure in the velocity field and if the velocity field is temporally quasi-regular. This spatial structure is manifested in the form of “cat’s eyes” in the surf zone, such as are commonly seen in numerical simulations of Rossby wave critical layers; by analogy with the heteroclinic structure of a temporally aperiodic chaotic system the cat’s eyes may be thought of as an “organizing structure” for mixing and transport in the surf zone. When this organizing structure exists, Eulerian and Lagrangian autocorrelations of the velocity derivatives indicate that velocity derivatives decorrelate more rapidly along particle trajectories than at fixed spatial locations (i.e., th... Abstract The relevance of chaotic advection to stratospheric mixing and transport is addressed in the context of (i) a numerical model of forced shallow-water flow on the sphere, and (ii) a middle-atmosphere general circulation model. It is argued that chaotic advection applies to both these models if there is suitable large-scale spatial structure in the velocity field and if the velocity field is temporally quasi-regular. This spatial structure is manifested in the form of “cat’s eyes” in the surf zone, such as are commonly seen in numerical simulations of Rossby wave critical layers; by analogy with the heteroclinic structure of a temporally aperiodic chaotic system the cat’s eyes may be thought of as an “organizing structure” for mixing and transport in the surf zone. When this organizing structure exists, Eulerian and Lagrangian autocorrelations of the velocity derivatives indicate that velocity derivatives decorrelate more rapidly along particle trajectories than at fixed spatial locations (i.e., th...