Numerical solution of the dispersion equation using a variable dispersion coefficient: method and applications

ABSTRACT

The study presented herein forms part of a wider research project on dispersion prediction in open channel flows which include laboratory, field and numerical investigations. In this paper, a numerical model which uses finite elements in space and finite differences in time for the solution of the convective-dispersion equation is developed and verified. In the model, the dispersion coefficient is considered as a function of time (or distance) during the initial period. It is represented by a modified Fickian type model which has been calibrated by the authors using laboratory data. The numerical model has been used to predict concentration profiles of tracer studies carried out in the laboratory as well as in the field.     

Studies on turbulent diffusion processes and evaluation of diffusivity values from hydrodynamic observations in Corpus Christi Bay

The physical process of dispersion which can be attributed to turbulence (turbulent diffusion) or shear (shear-augmented diffusion) within the flow field is very important as it ultimately governs the distribution of constituents of interest within the environment. A series of diffusion experiments were conducted in Corpus Christi Bay, TX with the purpose of characterizing turbulent diffusion through dispersion coefficients or turbulent diffusivity, K_i (i=x, y, z) dependent on the degree of randomness or turbulence intensity, I.Measured with a boat-mounted acoustic doppler current profiler (ADCP), the Eulerian velocity time-series of fluid particles in random motion, u_i was used in the evaluation of the Eulerian time-scale of turbulence, T^E based on the velocity correlation function, R^E with T^E being related to the Lagrangian time-scale T^L through a scaling parameter, β(=T^L/T^E). Surface currents were obtained with high frequency (HF) Radar equipment deployed over the study area from which the horizontal velocity gradients were determined.Within the spatial scale of the experiment (1000 m), the observed low horizontal gradients (10⁻⁴ s⁻¹) allowed for the generation of velocity time-series from an ADCP mounted on a moving platform. A numerical scheme for evaluating turbulent diffusivity values was developed on the basis of Eulerian current measurements and calibrated through the statistics of an evolving dye patch for the scaling parameter β which in this scheme was found to be in the range 1–3.     

THE ELECTRICAL CURRENT PATTERN INDUCED BY AN OSCILLATING MAGNETIC DIPOLE IN A SEMI INFINITE CONDUCTIVE THIN PLATE*

In a paper by Koefoed and Kegge (1968), which was based on previous work of Wesley (1958), the electrical current pattern has been derived that is induced by an oscillating magnetic dipole in a semi-infinite thin plate of infinitesimal resistivity. In the present paper, the range of validity of the assumptions, on which the work of Wesley is based, is subjected to a theoretical analysis. It is found that the decisive factor for the validity of Wesley's derivation is the quotient of the square of the penetration depth of the electrical current over the product of the thickness of the plate and a distance that is indicative of the size of the current loops in the plate. Wesley's derivation is shown to be valid only when this factor is negligible. It is also shown that in this condition the imaginary component of the anomaly must be negligible. Model experiments are described in which the electrical current pattern is studied also in the range in which the derivation of Wesley is not valid. The procedure used in these model experiments was to measure the tangential component of the magnetic field strength very close to the metal plate that simulated the conductive dyke. In order to express the results of the measurements in terms of the imaginary to real ratio, these results are compared with an interpretation graph for field measurements that was published by Hedström and Parasnis (1958). It is found that the current pattern in the plate is essentially the same as that which follows from Wesley's derivation, provided that the imaginary to real ratio is less than one third. The measurements do not permit to draw conclusions regarding the current pattern in the plate in conditions that correspond to larger values of the imaginary to real ratio.     

Geologic evolution of the Canarian Islands of Lanzarote, Fuerteventura, Gran Canaria and La Gomera and comparison of landslides at these islands with those at Tenerife, La Palma and El Hierro

In this paper we discuss the results of a swath bathymetric investigation of the Canary archipelago offshore area. These new data indicate that volcanism is pervasive throughout the seafloor in the region, much more that would be suggested by the islands. We have mapped tens of volcanic edifices between Fuerteventura and Gran Canaria and offshore Tenerife, La Gomera, El Hierro and La Palma. Volcanic flows are present between Tenerife and La Gomera and salic necks dominate the eastern insular slope of La Gomera. This bathymetry also supports land geologic studies that indicate that the oceanic archipelago has acquired its present morphology in part by mass wasting, a consequence of the collapse of the volcanic edifices. In the younger islands, Tenerife, La Palma and El Hierro, the Quaternary (1.2 to 0.15 Ma) debris avalanches are readily recognizable and can be traced offshore for distances measured in tens of km. Off the older islands, Lanzarote, Fuerteventura, Gran Canaria and La Gomera (<20 to 3.5 Ma), the avalanches have been obscured by subsequent turbidity current deposition and erosion as well as hemipelagic processes. The failure offshore western Lanzarote is in the form of a ramp at the base of the insular slope bound on the seaward side by a scarp. Its size and the lack of evidence of rotation along its landwards side precludes the possibility that it is a slump. It probably represents a slide whose outer scarp is caused by break-up of the slide. Mounds on the ramp’s surface may represent post-displacement volcanic structures or exotic blocks transported to their present locations by the slide. The failures offshore Fuerteventura are so large that, although they occurred in the Miocene-Pliocene, exotic blocks displaced from upslope are still recognizable in the insular margin morphology. The Canary Island insular margin appears to be a creation of Miocene-Pliocene mass wasting and more recent turbidity current deposition and erosion, and hemilepagic deposition. Failures offshore La Gomera are due to debris flows and/or turbidity currents. These events have obscured earlier mass wasting events. An erratum to this article is available at .     

Early Paleozoic gabbro-granitoid associations in eastern segment of the Mongolian-Okhotsk foldbelt (Amur River basin): Age and tectonic position

Magmatic rocks of the Pikan and Un’ya massifs situated in eastern segment of the Mongolian-Okhotsk foldbelt are studied using isotopic-geochronological (U-Pb zircon dating) and geochemical methods. Two rock complexes different in age are recognized in the Pikan massif: the high-Al gabbro-tonalite association of the Middle Ordovician (468 ± Ma) and granodiorite-granite association of the Late Silurian-Early Devonian (415 ± 7 Ma). The Late Ordovician age (454 ± 5 Ma) is established for leucocratic granites of the Un’ya massif. As is suggested, the Pikan and Un’ya massifs are “allogenic blocks” detached from continental framework of the Mongolian-Okhotsk foldbelt and tectonically emplaced into the foldbelt structure at the last stage of its development.     

Ichnology of Bhuban and Boka Bil Formations,oligocene-miocene deposits of Manipur Western Hill,Northeast India

Oligocene-Miocene deposits of Bhuban and Boka Bil Formations, Surma Group, Manipur Western Hill consist of well preserved ichnofossil assemblages. These formations are represented by eight lithofacies such as Massive sandstone (Sm), Rippled marked argillaceous sandstone (Sr), Wavy laminated sandstone-siltstone-silty shale (Sw), Laminated shale (Fl), Massive mudstone (Fm), Trough cross-bedded sandstone (St), Lenticular laminated sandstonesiltstonesilty shale (Sll) and Laminated to massive sandstone-siltstone (Ssc). Fifteen ichnospecies were identified, which further categories into Skolithos, Cruziana, and Skolithos/Cruziana ichnofacies. Overall distribution pattern and behavioural nature of the ichnoassemblage and sedimentological attributes suggests that the sediments of Bhuban and Boka Bil Formations were deposited under frequent fluctuating sea level, moderate to strong energy condition, subtidal to lower intertidal environment, rich in organic nutrients.     

Aeolian dune migration along the Ceará coast, north-eastern Brazil

Aeolian dune dimensions and migration rates are analysed along the Ceará coast, north-east Brazil. Dunes that are currently mobile along the Ceará coast are composed of barchans and sand sheets. The results show that barchans maintain an equilibrium form, which can be characterized by values of dimensionless shape parameters H/W and W/L , where H is the dune height, W is the wing-to-wing width and L is the dune length. Dunes are highly mobile, with average migration rates of 17·5 m year⁻¹ for barchans and 10 m year⁻¹ for sand sheets. The calculated migration rates were found to depend strongly on dune dimensions for both barchans and sand sheets, i.e. the larger the dune is, the lower the migration rate will be. This size dependence was associated with the existence of a representative common transport rate along the dune fields, which induces a different dune migration rate dependent on dune size. Finally, from the observed dune evolution, an aggregated scale aeolian sediment transport was inferred. This bulk transport rate, of the order of 90–100 m³ m⁻¹ year⁻¹, is only valid for a timescale of years to decades, which is the timescale used in dune evolution analysis.