The velocity field of homogeneous isotropic turbulence is simulated by a large number (38–1200) of random Fourier modes varying in space and time over a large number (> 100) of realizations. They are chosen so that the flow field has certain properties, namely (i) it satisfies continuity, (ii) the two-point Eulerian spatial spectra have a known form (e.g. the Kolmogorov inertial subrange), (iii) the time dependence is modelled by dividing the turbulence into large- and small-scales eddies, and by assuming that the large eddies advect the small eddies which also decorrelate as they are advected, (iv) the amplitudes of the large- and small-scale Fourier modes are each statistically independent and each Gaussian. The structure of the velocity field is found to be similar to that computed by direct numerical simulation with the same spectrum, although this simulation underestimates the lengths of tubes of intense vorticity.Some new results and concepts have been obtained using this kinematic simulation: (a) for the inertial subrange (which cannot yet be simulated by other means) the simulation confirms the form of the Eulerian frequency spectrum $\phi^{\rm E}_{11} = C^{\rm E}\epsilon^{\frac{2}{3}}U^{\frac{2}{3}}_0\omega^{-\frac{5}{3}}$, where ε,U0,ω are the rate of energy dissipation per unit mass, large-scale r.m.s. velocity, and frequency. For isotropic Gaussian large-scale turbulence at very high Reynolds number, CE ≈ 0.78, which is close to the computed value of 0.82; (b) for an observer moving with the large eddies the ‘Eulerian—Lagrangian’ spectrum is ϕEL11 = CELεω−2, where CEL ≈ 0.73; (c) for an observer moving with a fluid particle the Lagrangian spectrum ϕL11 = CLεω−2, where CL ≈ 0.8, a value consistent with the atmospheric turbulence measurements by Hanna (1981) and approximately equal to CEL; (d) the mean-square relative displacement of a pair of particles 〈Δ2〉 tends to the Richardson (1926) and Obukhov (1941) form 〈Δ2〉 = GΔεt3, provided that the subrange extends over four decades in energy, and a suitable origin is chosen for the time t. The constant GΔ is computed and is equal to 0.1 (which is close to Tatarski's 1960 estimate of 0.06); (e) difference statistics (i.e. displacement from the initial trajectory) of single particles are also calculated. The exact result that Y2 = GYεt3 with GY = 2πCL is approximately confirmed (although it requires an even larger inertial subrange than that for 〈Δ2〉). It is found that the ratio [Rscr ]G = 2〈Y2〉/〈Δ2〉≈ 100, whereas in previous estimates [Rscr ]G≈ 1, because for much of the time pairs of particles move together around vortical regions and only separate for the proportion of the time (of O(fc)) they spend in straining regions where streamlines diverge. It is estimated that [Rscr ]G ≈ O(fc−3). Thus relative diffusion is both a ‘structural’ (or ‘topological’) process as well as an intermittent inverse cascade process determined by increasing eddy scales as the particles separate; (f) statistics of large-scale turbulence are also computed, including the Lagrangian timescale, the pressure spectra and correlations, and these agree with predictions of Batchelor (1951), Hinzc (1975) and George et al. (1984).

The Pearl River Delta (PRD) region, located in the southern part of Guangdong Province in China, is one of the most rapidly developing regions in the world. The evolution of local and regional sea-breeze circulation (SBC) is believed to be responsible for forming meteorological conditions for high air-pollution episodes in the PRD. To understand better the impacts of urbanization and its associated urban heat island (UHI) on the local- and regional-scale atmospheric circulations over PRD, a number of high-resolution numerical experiments, with different approaches to treat the land surface and urban processes, have been conducted using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). The results show that an accurate urban land-use dataset and a proper urban land-use parameterization are critical for the mesoscale model to capture the major features of the observed UHI effect and land–sea-breeze circulations in the PRD. Stronger UHI in the PRD increases the differential temperature gradient between urbanized areas and nearby ocean surface and hence enhances the mesoscale SBC. The SBC front consequently penetrates farther inland to overcome the prevailing easterly flow in the western part of inland Hong Kong. Additional sensitivity studies indicate that further industrial development and urbanization will strengthen the daytime SBC as well as increase the air temperature in the lowest 2 km of the atmosphere.

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[1] Recent satellite observations show that a layer of haze perpetually hangs over the Pearl River Delta (PRD) region and surface observations show numerous violations of the Hong Kong Air Quality Objective. This layer of haze mostly concentrates in the Pearl River Estuary and a narrow (20 km wide) band along the shoreline, in particular during weak wind situations. Although researchers suspect the land-sea breeze (LSB) circulations ''concentrate'' or ''trap'' various pollutants in this region, the physical mechanism of the phenomenon has never been fully explained or quantified. In this paper, a mesoscale atmospheric model (MM5) coupled with the Noah land surface model (LSM), which has bulk urban land use treatments along with a detailed Pearl River Delta land use map, is used to investigate the unique feature and mechanism of this land-sea breeze effect and the temporal evolution. A three-dimensional particle trajectory model is used to understand its associated pollutant transport, trapping and accumulation. A conceptual model is then developed for the perpetual air pollution phenomenon in the region. Further sensitivity experiments are used to illustrate the impact of urbanization and large-scale winds on the pollution processes. Results show that urbanization enhances the pollutant trapping and therefore contributes to the overall poor air quality in the region.

Doppler wind LiDAR (Light Detection And Ranging) makes use of the principle of optical Doppler shift between the reference and backscattered radiations to measure radial velocities at distances up to several kilometers above the ground. Such instruments promise some advantages, including its large scan volume, movability and provision of 3-dimensional wind measurements, as well as its relatively higher temporal and spatial resolution comparing with other measurement devices. In recent decades, Doppler LiDARs developed by scientific institutes and commercial companies have been well adopted in several real-life applications. Doppler LiDARs are installed in about a dozen airports to study aircraft-induced vortices and detect wind shears. In the wind energy industry, the Doppler LiDAR technique provides a promising alternative to in-situ techniques in wind energy assessment, turbine wake analysis and turbine control. Doppler LiDARs have also been applied in meteorological studies, such as observing boundary layers and tracking tropical cyclones. These applications demonstrate the capability of Doppler LiDARs for measuring backscatter coefficients and wind profiles. In addition, Doppler LiDAR measurements show considerable potential for validating and improving numerical models. It is expected that future development of the Doppler LiDAR technique and data processing algorithms will provide accurate measurements with high spatial and temporal resolutions under different environmental conditions.

I investigate whether, in general, the average settling velocity of a small particle/bubble subject to a square drag force in homogeneous, stationary turbulence with a Kolmogorov spectrum differs from that in still fluid and, in particular, the role played by the structures of the flow field. I study particle or bubble trajectories in a simple flow structure. Statistics have been computed for the motion of small particles/bubbles settling under gravity with a Gaussian random velocity generated by Fourier modes. As a main result it is shown that homogeneous turbulence does cause a net decrease of settling velocity in the case VT/U' "• 0(1). 1. 20,287 20,288 FUNG: GRAVITATIONAL SETTLING OF PARTICLES AND BUBBLES

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We study the topology, and in particular the'self-similar and space-filling properties of the topology of line-interfaces passively advected by five different 2-D turbulent-like velocity fields. Special attention is given to three fundamental as'pects of the flow: the time unsteadiness,'the classification of local spatial flow structure in'terms of hyperbolic and elliptic points borrowed from the study of phase spaces in dynamical systems and a classification of flow structure in wavenumbe; space derived from the studies of Weierstrass and related functions. The methods of analysis are based on a classification of interfacial scaling topologies in terms of K-and H-fractals, and on two interfacial scaling exponents, the Kolmogorov capacity QK and the dimension D introduced by Fung and Vassilicos [Phys. Fluids 11, 2725 (1991)] who conjectured that D> 1 implies that the interface is H-fractal. An argument is presented (in the Appendix) to show that D > 1 is a necessary condition for the evolving interface to be 'H-fractal through the action of the flow, and' that D> 1 is also sufficient provided that no isolated regions exist where the flow velocity is either unbounded or undefined in finite time. D is interpreted to be a degree of H-fractality and is different from the Hausdorff dimension D,. In all our flows, steady and unsteady, interfaces in particular realisations of the flow reach a non-space-filling steady self-similar state where D and DK are both constant in time even though the interface continues to be advected and deformed by the flow. It is found that D is equal to 1 in 2-D steady flows and always increases with unsteadiness, that DR generally decreases with unsteadiness where the interfacial topology is dominated by spirals, and that D, increases with unsteadiness where the interfacial topology is dominated by tendrils. In those flows with larger number of modes, DK is a non-increasing function of unsteadiness and a decreasing function of the exponent p of the tlow's self-similar energy spectrum E(k)-kmP. D,'s decreasing dependences on unsteadiness and the exponent p can be explained by the presence of spirals in the eddy regions of the flow. The values of D and D, and their dependence on unsteadiness can change significantly only by changing the distribution of wavenumbers in wavenumber space while keeping the phases and energy spectrum constant.