Very short-lived brominated substances (VSLBr) are an important source of stratospheric bromine, an effective ozone destruction catalyst. However, the accurate estimation of the organic and inorganic partitioning of bromine and the input to the stratosphere remains uncertain. Here, we report near-tropopause measurements of organic brominated substances found over the tropical Pacific during the NASA Airborne Tropical Tropopause Experiment campaigns. We combine aircraft observations and a chemistry−climate model to quantify the total bromine loading injected to the stratosphere. Surprisingly, despite differences in vertical transport between the Eastern and Western Pacific, VSLBr (organic + inorganic) contribute approximately similar amounts of bromine [∼6 (4−9) parts per thousand] to the stratospheric input at the tropical tropopause. These levels of bromine cause substantial ozone depletion in the lower stratosphere, and any increases in future abundances (e.g., as a result of aquaculture) will lead to larger depletions.

We have performed numerical simulations of inertial particles in random model flows in the white-noise limit (at zero Kubo number, Ku = 0) and at finite Kubo numbers. Our results for the moments of relative inertial-particle velocities are in good agreement with recent theoretical results (Gustavsson and Mehlig 2011a) based on the formation of phase-space singularities in the inertialparticle dynamics (caustics). We discuss the relation between three recent approaches describing the dynamics and spatial distribution of inertial particles suspended in turbulent flows: caustic formation, real-space singularities of the deformation tensor and random uncorrelated motion. We discuss how the phaseand real-space singularities are related. Their formation is well understood in terms of a local theory. We summarise the implications for random uncorrelated motion.

A full Lagrangian method (FLM) is used in direct numerical simulations (DNS) of incompressible homogeneous isotropic and statistically stationary turbulent flow to measure the statistical properties of the segregation of small inertial particles advected with Stokes drag by the flow. Qualitative good agreement is observed with previous kinematic simulations (KS) (IJzermans, Meneguz & Reeks, J. Fluid Mech., vol. 653, 2010, pp. 99–136): in particular, the existence of singularities in the particle concentration field and a threshold value for the particle Stokes number $\mathit{St}$ above which the net compressibility of the particle concentration changes sign (from compression to dilation). A further KS analysis is carried out by examining the distribution in time of the compression of an elemental volume of particles, which shows that it is close to Gaussian as far as the third and fourth moments but non-Gaussian (within the uncertainties of the measurements) for higher-order moments when the contribution of singularities in the tails of the distribution increasingly dominates the statistics. Measurements of the rate of occurrence of singularities show that it reaches a maximum at $\mathit{St}\ensuremath{\sim} 1$, with the distribution of times between singularities following a Poisson process. Following the approach used by Fevrier, Simonin & Squires (J. Fluid Mech., vol. 553, 2005, pp. 1–46), we also measured the random uncorrelated motion (RUM) and mesoscopic components of the compression for $\mathit{St}= 1$ and show that the non-Gaussian highly intermittent part of the distribution of the compression is associated with the RUM component and ultimately with the occurrence of singularities. This result is consistent with the formation of caustics (Wilkinson et al. Phys. Fluids, vol. 19, 2007, p. 113303), where the activation of singularities precedes the crossing of trajectories (RUM).

The results presented here are part of a long-term study in which we analyse the segregation of inertial particles in turbulent flows using the so called full Lagrangian method (FLM) to evaluate the ‘compressibility’ of the particle phase along a particle trajectory. In the present work, particles are advected by Stokes drag in a random flow field consisting of counter-rotating vortices and in a flow field composed of 200 random Fourier modes. Both flows are incompressible and, like turbulence, have structure and a distribution of scales with finite lifetime. The compressibility is obtained by first calculating the deformation tensor Jij associated with an infinitesimally small volume of particles following the trajectory of an individual particle. The fraction of the initial volume occupied by the particles centred around a position x at time t is denoted by |J|, where J ≡ det(Jij) and Jij ≡ ∂xi(x0, t)/∂x0,j, x0 denoting the initial position of the particle. The quantity d〈ln|J|〉/dt is shown to be equal to the particle averaged compressibility of the particle velocity field 〈∇ · v〉, which gives a measure of the rate-of-change of the total volume occupied by the particle phase as a continuum. In both flow fields the compressibility of the particle velocity field is shown to decrease continuously if the Stokes number St (the dimensionless particle relaxation time) is below a threshold value Stcr, indicating that the segregation of particles continues indefinitely. We show analytically and numerically that the long-time limit of 〈∇ · v〉 for sufficiently small values of St is proportional to St2 in the flow field composed of random Fourier modes, and to St in the flow field consisting of counter-rotating vortices. If St > Stcr, however, the particles are ‘mixed’. The level of mixing can be quantified by the degree of random uncorrelated motion (RUM) of particles which is a measure of the decorrelation of the velocities of two nearby particles. RUM is zero for fluid particles and increases rapidly with the Stokes number if St > Stcr, approaching unity for St ≫ 1. The spatial averages of the higher-order moments of the particle number density are shown to diverge with time indicating that the spatial distribution of particles may be very intermittent, being associated with non-zero values of RUM and the occurrence of singularities in the particle velocity field. Our results are consistent with previous observations of the radial distribution function in Chun et al. (J. Fluid Mech., vol. 536, 2005, p. 219).