Wind-tunnel modelling of dispersion from a scalar area source in urban-like roughness

A wind-tunnel study was conducted to investigate ventilation of scalars from urban-like geometries at neighbourhood scale by exploring two different geometries a uniform height roughness and a non-uniform height roughness, both with an equal plan and frontal density of λ p = λ f = 25%. In both configurations a sub-unit of the idealized urban surface was coated with a thin layer of naphthalene to represent area sources. The naphthalene sublimation method was used to measure directly total area-averaged transport of scalars out of the complex geometries. At the same time, naphthalene vapour concentrations controlled by the turbulent fluxes were detected using a fast Flame Ionisation Detection (FID) technique. This paper describes the novel use of a naphthalene coated surface as an area source in dispersion studies. Particular emphasis was also given to testing whether the concentration measurements were independent of Reynolds number. For low wind speeds, transfer from the naphthalene surface is determined by a combination of forced and natural convection. Compared with a propane point source release, a 25% higher free stream velocity was needed for the naphthalene area source to yield Reynolds-number-independent concentration fields. Ventilation transfer coefficients w T /U derived from the naphthalene sublimation method showed that, whilst there was enhanced vertical momentum exchange due to obstacle height variability, advection was reduced and dispersion from the source area was not enhanced. Thus, the height variability of a canopy is an important parameter when generalising urban dispersion. Fine resolution concentration measurements in the canopy showed the effect of height variability on dispersion at street scale. Rapid vertical transport in the wake of individual high-rise obstacles was found to generate elevated point-like sources. A Gaussian plume model was used to analyse differences in the downstream plumes. Intensified lateral and vertical plume spread and plume dilution with height was found for the non-uniform height roughness

Second order accurate upwind difference schemes for scalar conservation laws with source terms

A second order accurate, characteristic-based, finite difference scheme is developed for scalar conservation laws with source terms. The scheme is an extension of well-known second order scalar schemes for homogeneous conservation laws. Such schemes have proved immensely powerful when applied to homogeneous systems of conservation laws using flux-difference splitting. Many application areas, however, involve inhomogeneous systems of conservation laws with source terms, and the scheme presented here is applied to such systems in a subsequent paper.

A n-Bit Reconfigurable Scalar Quantiser

A reconfigurable scalar quantiser capable of accepting n-bit input data is presented. The data length n can be varied in the range 1... N-1 under partial-run time reconfiguration, p-RTR. Issues as improvement in throughput using this reconfigurable quantiser of p-RTR against RTR for data of variable length are considered. The quantiser design referred to as the priority quantiser PQ is then compared against a direct design of the quantiser DIQ. It is then evaluated that for practical quantiser sizes, PQ shows better area usage when both are targeted onto the same FPGA. Other benefits are also identified.

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

This paper concerns the switching on of two-dimensional time-harmonic scalar waves. We first review the switch-on problem for a point source in free space, then proceed to analyse the analogous problem for the diffraction of a plane wave by a half-line (the ‘Sommerfeld problem’), determining in both cases the conditions under which the field is well-approximated by the solution of the corresponding frequency domain problem. In both cases the rate of convergence to the frequency domain solution is found to be dependent on the strength of the singularity on the leading wavefront. In the case of plane wave diffraction at grazing incidence the frequency domain solution is immediately attained along the shadow boundary after the arrival of the leading wavefront. The case of non-grazing incidence is also considered.

Dispersion of a point-source release of a passive scalar through an urban-like array for different wind directions

The dispersion of a point-source release of a passive scalar in a regular array of cubical, urban-like, obstacles is investigated by means of direct numerical simulations. The simulations are conducted under conditions of neutral stability and fully rough turbulent flow, at a roughness Reynolds number of Reτ = 500. The Navier–Stokes and scalar equations are integrated assuming a constant rate release from a point source close to the ground within the array. We focus on short-range dispersion, when most of the material is still within the building canopy. Mean and fluctuating concentrations are computed for three different pressure gradient directions (0◦ , 30◦ , 45◦). The results agree well with available experimental data measured in a water channel for a flow angle of 0◦ . Profiles of mean concentration and the three-dimensional structure of the dispersion pattern are compared for the different forcing angles. A number of processes affecting the plume structure are identified and discussed, including: (i) advection or channelling of scalar down ‘streets’, (ii) lateral dispersion by turbulent fluctuations and topological dispersion induced by dividing streamlines around buildings, (iii) skewing of the plume due to flow turning with height, (iv) detrainment by turbulent dispersion or mean recirculation, (v) entrainment and release of scalar in building wakes, giving rise to ‘secondary sources’, (vi) plume meandering due to unsteady turbulent fluctuations. Finally, results on relative concentration fluctuations are presented and compared with the literature for point source dispersion over flat terrain and urban arrays. Keywords Direct numerical simulation · Dispersion modelling · Urban array

A tale of two elements: P1ncP1 and RTO

The and RT0 finite element schemes are among the most promising low order elements for use in unstructured mesh marine and lake models. They are both free of spurious elevation modes, have good dispersive properties and have a relatively low computational cost. In this paper, we derive both finite element schemes in the same unified framework and discuss their respective qualities in terms of conservation, consistency, propagation factor and convergence rate. We also highlight the impact that the local variables placement can have on the model solution. The main conclusion that we can draw is that the choice between elements is highly application dependent. We suggest that the element is better suited to purely hydrodynamical applications while the RT0 element might perform better for hydrological applications that require scalar transport calculations.

Upwind solution of singular differential equations arising from steady channel flows

We study ordinary nonlinear singular differential equations which arise from steady conservation laws with source terms. An example of steady conservation laws which leads to those scalar equations is the Saint–Venant equations. The numerical solution of these scalar equations is sought by using the ideas of upwinding and discretisation of source terms. Both the Engquist–Osher scheme and the Roe scheme are used with different strategies for discretising the source terms.

The cumulus-capped boundary layer. II: Interface fluxes

This paper considers the relationship between the mean temperature and humidity profiles and the fluxes of heat and moisture at cloud base and the base of the inversion in the cumulus-capped boundary layer. The relationships derived are based on an approximate form of the scalar-flux budget and the scaling properties of the turbulent kinetic energy (TKE) budget. The scalar-flux budget gives a relationship between the change in the virtual potential temperature across either the cloud base transition zone or the inversion and the flux at the base of the layer. The scaling properties of the TKE budget lead to a relationship between the heat and moisture fluxes and the mean subsaturation through the liquid-water flux. The 'jump relation' for the virtual potential temperature at cloud base shows the close connection between the cumulus mass flux in the cumulus-capped boundary layer and the entrainment velocity in the dry-convective boundary layer. Gravity waves are shown to be an important feature of the inversion.

The cumulus-capped boundary layer. I: Modelling transports in the cloud layer

Scalar-flux budgets have been obtained from large-eddy simulations (LESs) of the cumulus-capped boundary layer. Parametrizations of the terms in the budgets are discussed, and two parametrizations for the transport term in the cloud layer are proposed. It is shown that these lead to two models for scalar transports by shallow cumulus convection. One is equivalent to the subsidence detrainment form of convective tendencies obtained from mass-flux parametrizations of cumulus convection. The second is a flux-gradient relationship that is similar in form to the non-local parametrizations of turbulent transports in the dry-convective boundary layer. Using the fluxes of liquid-water potential temperature and total water content from the LES, it is shown that both models are reasonable diagnostic relations between fluxes and the vertical gradients of the mean fields. The LESs used in this study are for steady-state convection and it is possible to treat the fluxes of conserved thermodynamic variables as independent, and ignore the effects of condensation. It is argued that a parametrization of cumulus transports in a model of the cumulus-capped boundary layer should also include an explicit representation of condensation. A simple parametrization of the liquid-water flux in terms of conserved variables is also derived.

Effectiveness of landmark analysis for establishing locality in p2p networks

Locality to other nodes on a peer-to-peer overlay network can be established by means of a set of landmarks shared among the participating nodes. Each node independently collects a set of latency measures to landmark nodes, which are used as a multi-dimensional feature vector. Each peer node uses the feature vector to generate a unique scalar index which is correlated to its topological locality. A popular dimensionality reduction technique is the space filling Hilbert’s curve, as it possesses good locality preserving properties. However, there exists little comparison between Hilbert’s curve and other techniques for dimensionality reduction. This work carries out a quantitative analysis of their properties. Linear and non-linear techniques for scaling the landmark vectors to a single dimension are investigated. Hilbert’s curve, Sammon’s mapping and Principal Component Analysis have been used to generate a 1d space with locality preserving properties. This work provides empirical evidence to support the use of Hilbert’s curve in the context of locality preservation when generating peer identifiers by means of landmark vector analysis. A comparative analysis is carried out with an artificial 2d network model and with a realistic network topology model with a typical power-law distribution of node connectivity in the Internet. Nearest neighbour analysis confirms Hilbert’s curve to be very effective in both artificial and realistic network topologies. Nevertheless, the results in the realistic network model show that there is scope for improvements and better techniques to preserve locality information are required.