The 'problems' associated with analysing different kinds of turbulent flow and different methods of solution are classified and discussed with reference to how the turbulent structure in a flow domain depends on the scale and geometry of the domain's boundary, and on the information provided in the boundary conditions. Rapid distortion theory (RDT) is a method, based on linear analysis, for calculating 'rapidly changing turbulent' (RCT) flows under the action of different kinds of distortion, such as large-scale velocity gradients, the effects of bounding surfaces, body forces, etc. Recent developments of the theory are reviewed, including the criteria for its validity, and new solutions allowing for the effects of inhomogeneities and boundaries. We then consider the contribution of RDT to understanding the fundamental problems of 'slowly changing turbulent' (SCT) flows, such as why are similar and persistent features of the local eddy structure found in different kinds of shear flow, and what are the general features of turbulent flows near boundaries. These features, which can be defined in terms of certain statistical quantities and flow patterns in individual flow realizations, are found to correspond to the form of particular solutions of RDT which change slowly over the time of the distortion. The most general features are insensitive to the energy spectrum and to the initial anisotropy of the turbulence. A new RDT analysis of the energy spectra E(L) indicates why, in shear flows a t moderate Reynolds number, the turbulence tends to have similar forms of spectra for eddies on a local scale, despite the Reynolds number not being large enough for the existence of a nonlinear cascade and there being no universal forms of spectra for unsheared turbulence; for this situation, the action of shear dU,/dx, changes the form of the spectrum, so that, as /? = (tdU,/dx,) increases, over an increasing part of the spectrum defined in terms of the integral scale L by f ' >> k L , E (k) cc k-2, whatever the form of initial spectrum of E,(k) (provided E (k) = o(k-2) for kL B 1).

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Abstract. The Atmospheric Pollution and Human Health in a Chinese Megacity (APHH-Beijing) programme is an international collaborative project focusing on understanding the sources, processes and health effects of air pollution in the Beijing megacity. APHH-Beijing brings together leading China and UK research groups, state-of-the-art infrastructure and air quality models to work on four research themes: (1) sources and emissions of air pollutants; (2) atmospheric processes affecting urban air pollution; (3) air pollution exposure and health impacts; and (4) interventions and solutions. Themes 1 and 2 are closely integrated and support Theme 3, while Themes 1–3 provide scientific data for Theme 4 to develop cost-effective air pollution mitigation solutions. This paper provides an introduction to (i) the rationale of the APHH-Beijing programme and (ii) the measurement and modelling activities performed as part of it. In addition, this paper introduces the meteorology and air quality conditions during two joint intensive field campaigns – a core integration activity in APHH-Beijing. The coordinated campaigns provided observations of the atmospheric chemistry and physics at two sites: (i) the Institute of Atmospheric Physics in central Beijing and (ii) Pinggu in rural Beijing during 10 November–10 December 2016 (winter) and 21 May–22 June 2017 (summer). The campaigns were complemented by numerical modelling and automatic air quality and low-cost sensor observations in the Beijing megacity. In summary, the paper provides background information on the APHH-Beijing programme and sets the scene for more focused papers addressing specific aspects, processes and effects of air pollution in Beijing.

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Velocity fluctuations are calculated near an interface between a turbulent region and a stably stratified layer, and in the absence of mean shear. Based on the observation that the energy dissipation rate is finite in the turbulent region, a linear theory is constructed to match the given Eulerian (not Lagrangian) spectra of the turbulence in the turbulent region to the wave motion in the stable layer.The theory shows that eddies with frequency of the same order as the buoyancy frequency N of the stratified layer are least affected by the stratification. The mean square vertical velocity $\overline{\omega^2}\rightarrow 0$ when N → ∞, while ω2 is greatest at the interface when NLH/uH ≈ 2 uH and LH are respectively the velocity scale and longitudinal integral scale in the interior of the turbulent layer. In the stratified layer, since waves with frequency ω > N decay rapidly with distance z from the interface, the high-frequency parts of the spectra fall-off sharply, a striking feature of the atmospheric measurements of Caughey & Palmer (1979). In this inviscid model waves with frequency ω < N propagate in the stratified region without decay. The vertical integral scale Lx(w) is found to vary significantly with N, reaching a maximum at the interface when. NLH/uH ≈ 1. The wave energy flux (Fw) is a maximum when NLH/uH ≈ 6, a value frequently observed in the atmosphere.In the limit of large stratification (N → ∞), the theory shows that the effect of the stable layer on the turbulent region is the same as that of a rigid surface moving with the flow at the same mean velocity (i.e. the solution of Hunt & Graham 1978). Then. Fw → 0 and, at the interface, Lx(w) → 0. In the limit of small stratification (N → O) the vertical motion in the turbulent region decreases in intensity near the interface and irrotational motions are induced in the slightly stable layer (i.e. the same result as Phillips 1955).

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