An approximate analytical solution to the diffusion equation for short-range dispersion from a continuous ground-level source

An easily-evaluated expression for the dimensionless concentration profile (z/z ₀,/z ₀, z ₀/L) = = cu _*/kQ (or z ₀cu_*/kQ) downwind of a continuous ground-level area (or line) source in the stable surface layer is obtained by integrating the diffusion equation using the Shwetz approximation method (c = concentration, Q = source strength, k = von Kárman's constant). The analytical solution compares closely with concentration profiles obtained using a trajectory-simulation model over a useful range of heights, the important discrepancies occurring at the upper edge of the plume. The analytical solution is used to generate predictions of ground-level concentration for the Project Prairie Grass experiments; good agreement with the observations is obtained at all downwind distances (50 to 800 m).     

Statistics of atmospheric turbulence within and above a corn canopy

Two three-dimensional split-film anemometers were used to measure turbulence statistics within and above a corn canopy. Normalised profiles of mean windspeed, root-mean-square velocity, momentum flux, and heat flux were constructed from half-hourly averages by dividing within-canopy measurements by the simultaneous canopy-top measurement. With the exception of the heat flux, these profiles showed consistent shape from day to day. Time series of the three velocity components were recorded on magnetic tape and subsequently analysed to obtain Eulerian time and length scales and the power spectrum of each component at several heights. The timescale was found to have a local minimum value at the top of the canopy. However the length scale L _wformed from the timescale and the root-mean-square vertical velocity varied with height as L _w 0.1 z. The power-spectra were non-dimensionalised to facilitate comparison of spectra at different heights and times. All spectra had -5/3 regions spanning at least two decades in frequency.     

Turbulent dispersion in the atmospheric surface layer

By non-dimensionalizing a trajectory-simulation (TS) model of turbulent dispersion, it is shown that the dimensionless concentration z ₀cu_*/kQ (cu _*/kQ) due to a continuous line (area) source of strength Q in the atmospheric surface layer depends only on z/z ₀, x/z ₀, z ₀/L and z _s/z₀, where z _s is the source height. The TS model is used to tabulate concentration profiles due to ground-level line and area sources. Concentration profiles generated by the TS model for elevated sources are shown to be inconsistent with the Reciprocal Theorems of Smith (1957) and it is suggested that this is because the flux-mean gradient closure scheme inherent in the Reciprocal Theorem is invalid for an elevated source.     

Numerical simulation of particle trajectories in inhomogeneous turbulence,III: Comparison of predictions with experimental data for the atmospheric surface layer

It is shown that predictions of a numerical trajectory-simulation method agree closely with the Project Prairie Grass observations of the concentrations 100 m downwind of a continuous point source of sulphur dioxide if the height (z) dependence of the Lagrangian length scale Λ _L is chosen as: whereL is the Monin-Obukhov length. The value of 0.5 for Λ _L /z in neutral conditions is consistent with the findings of Reid (1979) for the Porton experiment, and is also shown to be the best choice for simulation of an experiment in which concentration profiles were measured a short distance (< 40 m) downwind of an elevated point source of glass beads (40 μn diameter). $$\begin{gathered} \Lambda _L = 0.5z\left( {1 - 6\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} L< 0 \hfill \\ \Lambda _L = 0.5z/\left( {1 + 5\frac{z}{L}} \right)L > 0 \hfill \\ \end{gathered} $$      

An ignimbrite veneer deposit: The trail-marker of a pyroclastic flow

The term “ignimbrite veneer deposit” (IVD) is proposed for a new kind of pyroclastic deposit which is found associated with, and passes laterally into, Taupo ignimbrite of valley pond type in New Zealand. It forms a thin layer mantling the landscape over 15,000 km², and is regarded as the deposit from the trailing “tail” of a pyroclastic flow, where a relaxation of shear stress favoured the deposition of the basal part of the flow. The IVD differs little in grain-size from the associated ignimbrite, but it shows a crude internal stratification attributed to the deposition of a succession of layers, one after the passage of each pulse of the pyroclastic flow. It locally contains laterally-discontinuous lenses of coarse pumice (“lee-side lenses”) on the far-vent side of topographic obstacles. In nearvent exposures the Taupo IVD shows lensoid and cross-stratified bed-forms even where it stands on a planar surface, attributed to deposition from a flow travelling at an exceedingly high velocity.An IVD can be distinguished from a poorly sorted pyroclastic fall deposit because the beds in it show more rapid lateral variations in thickness, it may show a low-angle cross-stratification, and it contains carbonised wood from trees not in the position of growth; from the deposit of a wet base surge because it lacks vesicles and strong antidune-like structures and contains carbonised vegetation, and from a hot and dry pyroclastic surge deposit because it possesses a high content of pumice and “fines”.The significance of an IVD is that it records the passage of a pyroclastic flow, where the flow itself has moved farther on.     

Relationships between pressure, volatile content and ejecta velocity in three types of volcanic explosion

Consideration of the energy equation for a flowing compressible fluid shows that the so-called modified Bernoulli equation, commonly used to relate ejects velocity to pre-explosion pressure in vulcanian-style volcanic explosions, is inadequate in almost all circumstances because of its neglect of the detailed role of volatiles in explosive eruptions.The physical differences between three common types of explosive volcanic activity, typified by plinian, strombolian and vulcanian events, are reviewed and simple mathematical models are proposed for them. The models relate velocities of ejects to initial pressures at the start of an explosive phase and to mass fractions of volatiles (generally taken to be water) in the explosion products. When fitted to observed ejects velocities (or velocities deduced from the dispersal of debris) up to 500 m/s the models predict pressures up to 300 bars — almost always much lower than those deduced in earlier treatments.     

Dynamic analysis by direct superposition of Ritz vectors

The solution of the eigenvalue problem for large structures is often the most costly phase of a dynamic response analysis. In this paper, the need for the exact solution of this large eigenvalue problem is eliminated. A new algorithm, based on error minimization, is presented for the generation of a sequence of Ritz vectors. These orthogonal vectors are used to reduce the size of the system. Only Ritz vectors with a large participation factor are used in the subsequent mode superposition analysis. In all examples studied, the superposition of Ritz vectors yields more accurate results, with fewer vectors, than if the exact eigenvectors are used. The proposed method not only reduces computer time requirements significantly but provides an error estimation for the dynamic analysis. The approach automatically includes the advantages of the proven numerical techniques of static condensation, Guyan reduction and static correction due to higher mode truncation.     

13C/12C ratio variations in Pinus longaeva (bristlecone pine) cellulose during the last millennium

δ¹³C values are presented for cellulose samples prepared from two dendrochronologically dated Pinus longaeva (bristlecone pine) trees which grew during the last 1000 years. δ¹³C variations for these lower forest border trees are similar to upper tree line ring-width variations for the same species and English high summer temperature variations for the same time period. However, the δ¹³C variations appear to be unrelated to lower forest border ring-width variations and cellulose δ D variations for the same specimens.     

From comparative statics to dynamics in urban-systems theory

An outline is presented of the main methods of systems analysis relevant to urban and regional modelling. The argument is set in the context of a brief discussion of system types and the identification of these for cities and regions. The methods are illustrated by reference to the Huff— Lakshmanan— Hansen shopping model with particular emphasis on developing techniques in dynamical systems theory.