Expanding Box Model Research Articles

Alfvén wave propagation and ion cyclotron interactions in the expanding solar wind: One‐dimensional hybrid simulations

We carry out one‐dimensional hybrid simulations of Alfvén waves propagating along the magnetic field in the presence of a mean radial spherically expanding plasma outflow, representing fast solar wind streams. The equations for particle ions of multiple species and fluid electrons are solved using the Expanding Box Model, a locally Cartesian representation of motion in spherical coordinates, in a frame moving with the local average wind speed. The model gives a minimally consistent description of the effects associated with such motion on particle dynamics, e.g., the flux‐conserving decrease of magnetic field intensity and consequent decrease of cyclotron frequency with increasing distance from the Sun. The cyclotron frequency decreases faster than Alfvén wave frequency, allowing fluctuations below the cyclotron frequency at smaller distance from the Sun to come into cyclotron resonance at greater distances. The hybrid treatment yields a fully self‐consistent description of the consequent cyclotron wave‐particle interaction in a multi‐ion plasma. We present results for cases of monochromatic circularly polarized Alfvén waves propagating radially outward and for initially well developed Alfvénic spectra with and without alpha particles. When both alpha particles and protons are present, the alpha particles, which come into resonance first as the wind expands, are observed to be preferentially heated and accelerated. For high beta (equal to ratio of ion pressure to magnetic field pressure) the amount of alpha particles acceleration and heating is limited by the available wave power. For low beta cases the amount of heating and acceleration is limited, not by the wave power, but by the depletion of the distribution function in the resonance region by pitch‐angle scattering. The implication of these results for solar wind models is discussed.

Factors influencing ozone chemistry in subsonic aircraft plumes

This study investigates several factors that could influence ozone chemistry occurring in subsonic aircraft plumes in the upper troposphere. The study focuses on uncertainties in gas-phase rate parameters, but also examines the influence of selected heterogeneous reactions, the rate of expansion of the plume, ambient and initial plume concentrations, and the time of emissions. Monte Carlo analysis with Latin hypercube sampling was applied to an expanding box model of an aircraft plume, in order to estimate the sensitivities of O 3 perturbations (ΔO 3) to uncertainties in rate constants in the RADM2 chemical mechanism. The resulting coefficient of variation in ΔO 3 at the end of a 36 h simulation was about 50%. Influential uncertainties in gas-phase rate parameters include those for photolysis of NO 2 and HCHO, O 3+NO, HO 2+NO, and formation of PAN and HNO 3. With high background concentrations of non-methane hydrocarbons, uncertainties in rate parameters of reactions involving peroxy radicals from ethene and propene oxidation were also influential. The coefficient of variation for ΔO 3 due to uncertainties in emission indices of NO x , CO, and organic compounds was less than 15%. The effects of the heterogeneous reaction of N 2O 5 leading to HNO 3 formation, and hypothesized reactions of HNO 3 and NO 2 on soot, were also investigated. The results suggest that the latter two reactions could be influential for ΔO 3 if published estimates of reaction probabilities and high estimates of soot concentrations in plumes are realistic.

Measurements of nitrogen oxides from aircraft in the northeast Atlantic flight corridor

We investigated the size and composition of exhaust plumes of commercial airliners in the northeast Atlantic flight corridor off the shores of Ireland and Scotland, an area with high air traffic density in the tropopause region. The primary objective was to measure the contribution of the NO and NOy emitted from aircraft to the nitrogen oxide background. We have made measurements in aircraft flight corridors by flying a research aircraft perpendicular to the routes of commercial transatlantic air traffic. Although previous studies had succeeded in identifying a few plumes, this study was the first systematic investigation of over 60 aircraft plumes through in situ NO and NOy measurements. These plumes were up to 1.5 km wide (along our flight paths) and showed NOy mixing ratios of up to 10 ppb above the background levels. The measurements showed that on larger scales the composition of NOy in the background air masses was very heterogeneous. On top of this natural variability of the NOy, we could not identify any influence of air traffic exhaust on air chemistry on scales larger than a few kilometers from our data. A secondary objective was to estimate the importance of the oxidation of NOχ to NOy in the relatively fresh plumes. The measured NO/NOy ratios were near the NO/NOχ ratios calculated from a simple photo‐stationary state assumption. This result was also consistent with calculations made with an expanding box model that included gas‐phase chemistry for the measured plume conditions. The model calculated NO/NOy and NC/NOχ ratios were almost equal, and these were consistent with the measured NO/NOy, ratios. These calculations showed that oxidation of NOχ to higher oxides played only a negligible role in our measured plumes of ages between 14 and 90 min.

Waves and streams in the expanding solar wind

The expanding box model (EBM) allows the simulation of the evolution of compressible MHD turbulence within the expanding solar wind, taking into account the basic properties of expansion. Using the EBM, we follow the evolution of waves within a compressive stream shear and magnetic sector structure in the range of 0.1 to 1 AU from the Sun. We analyze the physical processes which lead in these simulations to the modulation and erosion of the wave component, combined with WKB and non‐WKB processes due to expansion. A strong erosion by stream shear corresponds indeed to one of the observed regimes in the solar wind; however, we are unable to reproduce the regime which holds during solar minimum, in which the correlation between large‐scale stream structure and turbulence remains high independently from distance to the Sun. The main point of disagreement with observations concerns the energy spectrum (it is difficult to generate and sustain small‐scale turbulence with an Alfvénic wave band present, and even more so in an expanding medium); the main point of agreement concerns the statistics of density fluctuations, which are independent of distance, and matches the observed amplitudes both within slow and fast wind. At the same time, small scales appear to be dominated in the simulations by compressible effects, which contradicts popular ideas on solar wind turbulence.

The impact of local emissions on the formation of secondary pollutants in urban plumes

The results of modelling studies are reported together with a further analysis of an existing field measurement dataset. Emphasis is on the maximum ozone concentrations occurring in the urban plume from London, UK, on days of photochemical activity. Nitrogen oxide and volatile organic compound emissions from automotive exhausts are expected to be a large proportion of the total emission of these species, and the effect of their distinct diurnal variation is apparent in the field data. Factorial sensitivity studies on an expanding box model of the urban plume also show the dominance of urban emissions in the determination of plume maxima 100km downwind of the upwind urban boundary. These effects are not additive and depend strongly on the level of other variables.

Mixing models for the simulation of plume interaction with ambient air

This paper reports the development and evaluation of an improved treatment of the mixing of plume material with ambient air for use in reactive plume models, to examine the effects of dispersion in more detail. Two mixing schemes based upon a multiple expanding box model are examined. Previous work has shown that the rate of turbulent mixing of ambient material into a plume is of primary importance, and a major feature of the schemes considered is that they allow the plume boundary to be precisely defined, so that the ambient air may be treated as uniform and the flux of ambient material into the plume area precisely calculated. It is shown that these schemes, while not formulated in terms of diffusion, can be considered to be equivalent to finite difference approximations to the diffusion equation on an expanding grid. This use of an expanding grid is shown to lead to unconditionally stable equations which exhibit very little numerical diffusion. This allows the choice of timestep in a numerical integration to be governed by the chemistry. Tests performed using a full chemical scheme to control the timesteps show that the mixing schemes give excellent agreement with analytical solutions for passive tracers. The schemes thus provide a sound basis for the further investigation of the effect of entrainment on plume chemistry. Comparison of the results of reactive plume simulations using multiple and uniform expanding box models shows that it is the total amount of ambient air mixed into the plume which is of primary importance in determining total overall reaction, rather than the details of mixing within the plume.

The effect of a polluting source on the air quality downwind of pristine northern areas

The diurnal variations during summer and winter of the concentrations of NO, NO 2, O 3 and hydrocarbons downwind from a polluting source in pristine areas are calculated using a chemically oriented expanding box model. It is found that during the summer high ozone levels could be expected in the afternoon, particularly from a mixture originally emitted between 6 and 10 a.m. Under identical conditions high ozone levels are not predicted at any time of the day during the winter. HO 2NO 2 is predicted to be present at higher levels than PAN during the winter, whereas during summer the reverse situation obtains.