The shallow water equations on the sphere and their Lagrange-Galerkin-solution

Summary ?The shallow water equations are formulated on the sphere in a three-dimensional coordinate system with the aid of tangential velocity components and differential operators. We introduce a modified semi-Lagrangian scheme for the discretization in time. The discretization in space is solved by linear finite elements. The grids we use are regular refinements of a macro triangulation which itself is derived from a highly symmetric polyeder also known as a bucky or soccer ball. The good numerical results show that this combination is a promising approach. The numerical algorithm is stable and its strength is the conservation of mass and energy. Received April 13, 2001; Revised December 18, 2001     

Vibrationally excited molecular hydrogen in circumstellar clouds and the interstellar CH+ abundance

The production of CH⁺ in dense interstellar clouds under intense UV irradiation is discussed. A model applicable to the cloud towards the star 20 Tau is described.     

Aklimaite, Ca4[Si2O5(OH)2](OH)4 · 5H2O, a new natural hydrosilicate from Mount Lakargi, the Northern Caucasus, Russia

A new mineral aklimaite, Ca₄[Si₂O₅(OH)₂](OH)₄ · 5H₂O, has been found near Mount Lakargi, Upper Chegem caldera, Kabardino-Balkaria, the Northern Caucasus, Russia, in the skarnified limestone xenolith in ignimbrite. This hydrothermal mineral occurs in a cavity of altered larnite skarn and is associated with larnite, calcium humite-group members, hydrogarnets, bultfonteinite, afwillite, and ettringite. Aklimaite forms transparent, colorless (or occasionally with pinkish tint) columnar or lath-shaped crystals up 3 × 0.1 × 0.01 mm in size, flattened on {001} and elongated along {010}; they are combined in spherulites. The luster is vitreous; the cleavage parallel to the {001} is perfect. D _calc = 2.274 g/cm³. The Mohs’ hardness is 3–4. Aklimaite is optically biaxial, negative, 2V _meas > 70°, 2V _calc = 78°, α = 1.548(2), β = 1.551(3), γ = 1.553(2). The IR and Raman spectra are given. The chemical composition (wt %, electron microprobe) is as follows: 0.06 Na₂O, 0.02 K₂O, 45.39 CaO, 0.01 MnO, 0.02 FeO, 24.23 SiO₂, 0.04 SO₃, 3.22 F, 27.40 H₂O_(calc.), ?1.36 -O=F₂; the total is 99.03. The empirical formula calculated on the basis of 2Si apfu with O + OH + F = 16 is as follows: (Ca_4.02Na_0.01)_Σ4.03[Si_2.00O_5.07(OH)_1.93][(OH)_3.16F_0.84] _Σ4.00 · 5H₂O. The mineral is monoclinic, space group C2/m, a = 16.907(5), b = 3.6528(8), c = 13.068(4) Å, β = 117.25(4)·, V= 717.5(4) ų, Z = 2. Aklimaite is representative of the new structural type, the sorosilicate with disilicate groups [Si₂O₅(OH)₂]. The strongest reflections in the X-ray powder patterns [d, Å (hkl)] are: 11.64(100)(001), 2.948(32)(310, 203), 3.073(20) ( $\bar 404$ , $\bar 311$ ), 2.320(12)(005, 510), 2.901 (11)(004), 8.30(10) $\left( {\bar 201} \right)$ . The type specimen is deposited in the Fersman Mineralogical Museum, Russian Academy of Sciences, Moscow.     

Lagrangian measurements and modelling of fluid advection in the inner surf and swash zones

New laboratory and field data are presented on fluid advection into the swash zone. The data illustrate the region of the inner surf zone from which sediment can be directly advected into the swash zone during a single uprush, which is termed the advection length. Experiments were conducted by particle tracking in a Lagrangian reference frame, and were performed for monochromatic breaking waves, solitary bores, non-breaking solitary waves and field conditions. The advection length is normalised by the run-up length to give an advection ratio, A, and different advection ratios are identified on the basis of the experimental data. The data show that fluid enters the swash zone from a region of the inner surf zone that can extend a distance seaward of the bore collapse location that is approximately equal to half of the run-up length. This region is about eight times wider than the region predicted by the classical swash solution of Shen and Meyer [Shen, M.C., Meyer, R.E., 1963. Climb of a bore on a beach. Part 3. Runup. Journal of Fluid Mechanics 16, 113–125], as illustrated by Pritchard and Hogg [Pritchard, D., Hogg, A.J., 2005. On the transport of suspended sediment by a swash event on a plane beach. Coastal Engineering 52, 1–23]. Measured advection ratios for periodic waves show no significant trend with Iribarren number, consistent with self-similarity in typical swash flows. The data are compared to recent characteristic solutions of the non-linear shallow water wave (NLSW) equations and both finite difference and finite volume solutions of the NLSW equations.     

Incrustations and fumarolic condensates at kilauea volcano, Hawaii: field, drill-hole and laboratory observations

Hawaiian volcanoes characteristically have but few of the many types of minerals found in incrustations of other volcanic areas. In Hawaii sulfates resulting from air oxidation of volatiles predominate, and fluorides produced during rock alteration by fumarolic gases are prominent. Halides are generally found where reducing conditions exist in fumaroles and lava lake drill holes. The most common mineral types are sulfur, opaline silica, gypsum, ralstonite, and thenardite. Minerals from the same deposit are found to vary markedly in the content of the less abundant components. Condensates from vapor issuing from fumaroles show little quantitative relationship in component content to incrustations deposited at the same fumaroles. It is believed that an energetically favorable isomorphic substitution of some elements in the crystal lattice of a depositing mineral may lead to the build-up of a high concentration of an element from a lean vapor. Equilibrium calculations applied to condensate studies give a good quantitative approximation to the concentrations of the elements found in natural systems, but when applied to incrustations they serve only to indicate general compositional relations. Laboratory studies have shown the important role of chlorides in metal transfer in the gas phase in high-temperature aqueous systems, but only in the absence of oxygen. These studies also demonstrated the important role of HF in rock alteration and in the transfer of silica.     

Variations in statistical parameters of the <Emphasis Type="Italic">NmF</Emphasis>2 winter anomaly with latitude and solar activity

The maximal R ratios of the winter-to-summer NmF2 values of each ionosonde are calculated for a specified UT under daytime quiet geomagnetic conditions and at approximately equal levels of solar activity, based on foF2 measurement data of 98 ionosondes at mid- and low geomagnetic latitudes of the Northern and Southern hemispheres for 1957–2009. The P(R > 1) conditional probability of NmF2 winter anomaly observations, as well as the most probable RMP and average <R> of R values are calculated for low, moderate, and high solar activity on the base of foF2 measurements during the periods December 22 ± 30 days and June 21 ± 30 days. Variations in P(R > 1), RMP, and 〈R〉 with latitude and solar activity are analyzed.     

Marine microbiological studies of mangrove swamps of Killai backwaters

The bacterial populations of mangrove swamps of Killai backwaters (11°21–11°29N, 79°46–79°50E, South India) were studied during August 1968 (Pre monsoon period) and December (post monsoon period). The presence of these groups such as agar digesters, algin digesters, cellulose digesters, sulphate reducers etc., bring about transformation of organic matter in the mangrove swamps. The presence of denitrifiers in mangrove swamps and in association with the molluscs may bring about the precipitation of calcium carbonate by removing the acid radicals such as sulphate and nitrite, increasing alkalinity. The luminiscent bacteria such asVibrio andAeromonas were also isolated in mangrove swamps of Killai backwaters. The iron bacteria likeLeptothrix sp. andGallionella sp. were also isolated from mangrove swamps of Killai backwaters.     

Oil pollution of the anabranches of the Ob river on the territory of Khanty-Mansi Autonomous Okrug–Yugra

An analysis is made of the oil pollution of the Ob river waters using a long-term (1993–2013) hydrochemical monitoring of oil fields in Khanty-Mansi Autonomous Okrug. Contents of oil hydrocarbons (OHC) were determined in 4277 samples from the main Ob channel, and in 7076 samples from its anabranches by using infrared spectrometry. An increase in MAC (0.05 mg/dm³) was observed in 28% of the samples from the main channel, and in 32% from the anabranches. The total percentage of samples with an extremely high (> 50 MAC) and high (30–50 MAC) pollution level made up 0.3% of the samples for the anabranches, and 0.1% for the main channel. Maximum pollution was revealed in the eastern part of Okrug, from its eastern boundary to the mouth of the Trom’egan river which is associated with a considerable number of accidents on the pipelines within the Nizhnevartovskii district. The upper and lower quantiles in the most polluted anabranches, Pasl and Bagras, are 0.03–01.7 and 0.032–0.16 mg/dm³, respectively, whereas in the main Ob channel they vary from 0.022 to 0.065 mg/dm³ (0.4–1.2 MAC). The methods of geoinformatics and mathematical statistics were used to assess a dependence of OHC on the number of pollution sources (well clusters, and the area of oil spills) in zones at different distances from the river channels. By calculating the Spearman correlation coefficients, it was shown that OHC contents are dependent mainly on the number of wells, and on the area of oil spills located at less than 2 km from the channels.     

The Eastern Congo—a beauty spot,rediscovered from a geological point of view

In East Africa, the feedback between tectonic uplift, erosional denudation and associated possible climate changes is being studied by a multidisciplinary research group, ‘Riftlink’. The group's focus is the Albertine Rift, the northern part of the western branch of the East African Rift System, and in particular the rising Rwenzori Mountains that stretch along the border of the D.R. Congo and Uganda. Major questions relate to the timing of the formation of the Rwenzori Mountains, and whether the height of these mountains (> 5000 m) relates to rift movements in Neogene times, or represents an old basement block that formed a topographic high long before. Though, at first, research concentrated on the eastern (Ugandan) part of the Albertine Rift and Rwenzori Mountains, it has now moved further to the west to the D.R. Congo. A first field‐campaign, covering the area from northern Lake Edward along the rift shoulder up to the Blue Mountains at Lake Albert, was conducted in summer 2009, in cooperation with the Ruwenzori State University of Butembo. Here, we present a brief overview of the field‐campaign, with impressions gathered on the morphology and geology of the study area.     

A computer program for interpreting vertical magnetic anomalies of spheres and horizontal cylinders

Summary A common computer program for the interpretation of vertical magnetic anomalies of spheres and horizontal cylinders has been developed. The input consists of the observed anomalies noted against their distances measured from an arbitrary point in the profile and a code number for each model. The program is written so that the positions and magnitudes of the maximum and minimum anomalies are located and their ratios and signs are used to define the initial parameters of the model under consideration. The errors resulting from these approximate values are derived and are solved for the increments to be given to the initial values. The process is repeated until the sum of the squares of the errors is less than 0.25% of the sum of the squares of the observed anomalies. The method has been tested on various theoretical examples and the results justify the validity of the programme.