Abstract. We investigate the propagation of chemical fronts arising in Fisher-KolmogorovPetrovskii-Piskunov (FKPP) type models in the presence of a steady cellular flow. In the long-time limit, a steadily propagating pulsating front is established. Its speed, on which we focus, can be obtained by solving an eigenvalue problem closely related to large-deviation theory. We employ asymptotic methods to solve this eigenvalue problem in the limit of small molecular diffusivity (large Péclet number, Pe 1) and arbitrary reaction rate (arbitrary Damköhler number Da). We identify three regimes corresponding to the distinguished limits Da = O(Pe −1 ), Da = O (log Pe) −1 and Da = O(Pe) and, in each regime, obtain the front speed in terms of a different non-trivial function of the relevant combination of Pe and Da. Closed-form expressions for the speed, characterised by power-law and logarithmic dependences on Da and Pe and valid in intermediate regimes, are deduced as limiting cases. Taken together, our asymptotic results provide a complete description of the complex dependence of the front speed on Da for Pe 1. They are confirmed by numerical solutions of the eigenvalue problem determining the front speed, and illustrated by a number of numerical simulations of the advection-diffusion-reaction equation.

We investigate the influence of fluid flows on the propagation of chemical fronts arising in Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type models. We develop an asymptotic theory for the front speed in a cellular flow in the limit of small molecular diffusivity and fast reaction, i.e., large Péclet (Pe) and Damköhler (Da) numbers. The front speed is expressed in terms of a periodic path--an instanton--that minimizes a certain functional. This leads to an efficient procedure to calculate the front speed, and to closed-form expressions for (logPe)(-1) ≪ Da ≪ Pe and for Da ≫ Pe. Our theoretical predictions are compared with (i) numerical solutions of an eigenvalue problem and (ii) simulations of the advection-diffusion-reaction equation.

Abstract. The tropical tropopause layer (TTL) is a key region controlling transport between the troposphere and the stratosphere. The efficiency of transport across the TTL depends on the continuous interaction between the large-scale advection and the small-scale intermittent convection that reaches the Level of Zero radiative Heating (LZH). The wide range of scales involved presents a significant challenge to determine the sources of convection and quantify transport across the TTL. Here, we use a simple Lagrangian model, termed TTL detrainment model, that combines a large ensemble of 200-day back trajectory calculations with highresolution fields of brightness temperatures (provided by the CLAUS dataset) in order to determine the ensemble of trajectories that are detrained from convective sources. The trajectories are calculated using the ECMWF ERA-Interim winds and radiative heating rates, and in order to establish the radiative influence of clouds, the latter rates are derived both under all-sky and clear-sky conditions.We show that most trajectories are detrained near the mean LZH with the horizontal distributions of convective sources being highly-localized, even within the space defined by deep convection. As well as modifying the degree of source localization, the radiative heating from clouds facilitates the rapid upwelling of air across the TTL. However, large-scale motion near the fluctuating LZH can lead a significant proportion of trajectories to alternating clear-sky and cloudy regions, thus generating a large dispersion in the vertical transport times. The distributions of vertical transport times are wide and skewed and are largely insensitive to a bias of about Correspondence to: A. Tzella (a.tzella@ed.ac.uk) ±1 km (∓5 K) in the altitude of cloud top heights (the main sensitivity appearing in the times to escape the immediate neighbourhood of the LZH) while some seasonal and regional transport characteristics are apparent for times up to 60 days. The strong horizontal mixing that characterizes the TTL ensures that most air of convective origin is well-mixed within the tropical and eventually within the extra-tropical lower-stratosphere.