An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

An algorithm for the shallow water equations with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations in a generalised coordinate system. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme has good jump capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for flow past a circular obstruction.

Flux difference splitting for open channel flows

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow-water equations in open channels, together with an extension to two-dimensional flows. A linearized problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearized problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a one-dimensional dam-break problem, and to a problem of flow in a river whose geometry induces a region of supercritical flow. The scheme is also applied to a two-dimensional dam-break problem. The numerical results are compared with the exact solution, or other numerical results, where available.

Translation, decay and splitting of Agulhas rings in the southeastern Atlantic Ocean

All Agulhas rings that were spawned at the Agulhas retrofiec- tion between 1993 and 1996 (a total of 21 rings) have been monitored using TOPEX/Poseidon satellite altimetry and followed as they moved through the southeastern Atlantic Ocean, decayed, interacted with bottom topography and each other, or dissipated completely. Rings preferentially crossed the Walvis Ridge at its deepest parts. After having crossed this ridge they have lower translational speeds, and their decay rate decreases markedly. Half the decay of long-lived rings takes place in the first 5 months of their lifetimes. In addition to the strong decay of rings in the Cape Basin, about one third of the observed rings do not seem to leave this region at all but totally disintegrate here. The interaction of rings with bottom topography, in particular with the Verna Seamount, is shown frequently to cause splitting of rings. This will enhance mixing of the rings' Indian Ocean water into that of the southern Atlantic. This localized mixing may well provide a considerable source of warm and salty Indian Ocean water into the Atlantic overturning circulation.

Determination of pesticide residues in coconut water by liquid-liquid extraction and gas chromatography with electron-capture plus thermionic specific detection and solid-phase extraction and high-performance liquid chromatography with ultraviolet detection

Two simple methods were developed to determine, 11 pesticides in coconut water, a natural isotonic drink rich in salts, sugars and vitamins consumed by the people and athletes. The first procedure involves solid-phase extraction using Sep-Pak Vac C-18 disposable cartridges with methanol for elution. Isocratic analysis was carried out by means of high-performance liquid chromatography with ultraviolet detection at 254 nm to analyse captan, chlorothalonil, carbendazim, lufenuron and diafenthiuron. The other procedure is based on liquid-liquid extraction with hexane-dichloromethane (1:1, v/v), followed by gas chromatographic analysis with effluent splitting to electron-capture detection for determination of endosulfan, captan, tetradifon and trichlorfon and thermionic specific detection for determination of malathion, parathion-methyl and monocrotophos. The methods were validated with fortified samples at different concentration levels (0.01-12.0 mg/kg). Average recoveries ranged from 75 to 104% with relative standard deviations between 1.4 and 11.5%. Each recovery analysis was repeated at least five times. Limits of detection ranged from 0.002 to 2.0 mg/kg. The analytical procedures were applied to 15 samples and no detectable amounts of the pesticides were found in any samples under the conditions described. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Influence of muscle fiber orientation on water and metabolite relaxation times, magnetization transfer, and visibility in human skeletal muscle

PURPOSE To gain a deeper understanding of the influence of skeletal muscle fiber orientation on metabolite visibility, magnetization transfer from water, and water proton relaxation rates in (1) H MR spectra. METHODS Non-water-suppressed MR spectroscopy was performed in tibialis anterior muscle (TA) of 10 healthy adults, with the TA oriented either parallel or at the magic angle to the 3T field. Spectra were acquired with metabolite-cycled PRESS, and water inversion from 50 to 2510 ms before excitation. Water proton T2 relaxation was sampled with STEAM with echo times from 12 to 272 ms. RESULTS Apparent concentrations of total creatine (tCr), taurine, and trimethylammonium compounds were reduced by 29% to 67% when TA was parallel to B0 . Both tCr peak areas were strongly correlated to the methylene peak splitting. Magnetization transfer rates from water to tCr CH3 were not significantly different between orientations. Water T1 s were similar between orientations, but T2 s were statistically significantly shorter by 1 ms in the parallel orientation (P = 0.002). CONCLUSION Muscle metabolite visibilities in MR spectroscopy and water T2 times depend substantially on muscle fiber orientation relative to B0 . In contrast, magnetization transfer rates appear to depend on muscle composition, rather than fiber orientation. Magn Reson Med, 2015. © 2015 Wiley Periodicals, Inc.

Mass spectrometric determination of dioxygen bond splitting in the “peroxy” intermediate of cytochrome c oxidase

The “peroxy” intermediate (P form) of bovine cytochrome c oxidase was prepared by reaction of the two-electron reduced mixed-valence CO complex with 18O2 after photolytic removal of CO. The water present in the reaction mixture was recovered and analyzed for 18O enrichment by mass spectrometry. It was found that approximately one oxygen atom (18O) per one equivalent of the P form was present in the bulk water. The data show that the oxygen–oxygen dioxygen bond is already broken in the P intermediate and that one oxygen atom can be readily released or exchanged with the oxygen of the solvent water.