The low-pressure stability of phase A,Mg7Si2O8(OH)6

 Phase A, Mg₇Si₂O₈(OH)₆, is a dense hydrous magnesium silicate whose importance as a host of H₂O in the Earth’s mantle is a subject of debate. We have investigated the low-pressure stability of phase A in experiments on the reaction phase A=brucite+forsterite. Experiments were conducted in piston-cylinder and multi-anvil apparatus, using mixtures of synthetic phase A, brucite and forsterite. The reaction was bracketed between 2.60 and 2.75 GPa at 500° C, between 3.25 and 3.48 GPa at 600° C and between 3.75 and 3.95 GPa at 650^° C. These pressures are much lower than observed in the synthesis experiments of Yamamoto and Akimoto (1977). At 750^° C the stability field of brucite + chondrodite was entered. The enthalpy of formation and entropy of phase A at 1 bar (10⁵ Pa), 298 K, were derived from the experimental brackets on the reaction phase A=brucite+forsterite using a modified version of the thermodynamic dataset THERMOCALC of Holland and Powell (1990), which includes a new equation of state of H₂O derived from the molecular dynamics simulations of Brodholt and Wood (1993). The data for phase A are: ΔH ^o _f =−7126±8 kJ mol^-1, S ^o=351 J K^-1 mol^-1. Incorporating these data into THERMOCALC allows the positions of other reactions involving phase A to be calculated, for example the reaction phase A + enstatite=forsterite+vapour, which limits the stability of phase A in equilibrium with enstatite. The calculated position of this reaction (753° C at 7 GPa to 937° C at 10 GPa) is in excellent agreement with the experimental brackets of Luth (1995) between 7 and 10 GPa, supporting the choice of equation of state of H₂O used in THERMOCALC. Comparison of our results with calculated P-T paths of subducting slabs (Peacock et al. 1994) suggests that, in the system MgO–SiO₂–H₂O, phase A could crystallise in compositions with Mg/Si>2 at pressures as low as 3 GPa. In less Mg rich compositions phase A could crystallise at pressures above approximately 6 GPa. Received: 3 July 1995/Accepted: 14 December 1995     

MAGNETO-ATMOSPHERIC OSCILLATIONS IN A MODEL UMBRA

The behaviour of magneto-acoustic-gravity oscillations in a model umbra is investigated by means of a normal mode analysis. The normal modes are evaluated for different types of boundary conditions holding at various levels in the model atmosphere and for a range of magnetic field strengths and horizontal wave numbers. For certain boundary conditions complex eigenfrequencies are present. For atmospheric cavities whose lower boundary is located at the bottom of the photosphere or in the upper convective region, the coupling between horizontal and vertical motions leads to spectra which are sensitive to the value of the horizontal wave number, k, and the strength of the vertical magnetic field, B0. For cavities located above the temperature minimum, the eigenfrequencies are independent of both k and B0, supporting the conclusions of ugda, Locns, and Staude (1987) that the motion is longitudinal along the magnetic field lines. The frequencies evaluated from the normal mode analysis correspond closely to the observed 2–3-minute band found in sunspot umbrae.     

The onset of separation in neutral,turbulent flow over hills

The onset of separation in turbulent, neutrally stratified, boundary-layer flow over hills is considered. Since the flows are fully turbulent, the occurrence of intermittent separation, in the sense of any reversal of near surface flow, will depend strongly on the detailed structure and behaviour of the turbulent eddies. Very little is known about such intermittent separation and the phenomenon cannot be studied with numerical models employing standard turbulence closures; eddy-resolving models are required. Therefore, here, as elsewhere in the literature, the arguably less physically significant process of mean flow separation is studied. Numerical simulations of flow over idealised two- and three-dimensional hills are examined in detail to determine the lowest slope, _crit, for which the mean flow separates.Previous work has identified this critical slope as that required to produce a zero surface stress somewhere over the hill. This criterion, when a mixing-length turbulence closure is applied, reduces to requiring the near-surface vertical velocity shear to vanish at some point on the hill's surface. By applying results from a recent linear analysis for the flow perturbations to this condition, a new expression for _crit is obtained. The expression is approximate but its relative simplicity makes it practically applicable without the need for use of a computer or for detailed mapping of the hill. The approach suggested differs from previous ones in that it applies linear results to a non-linear expression for the surface stress. In the past, a linear expression for the surface stress has been used. The proposed expression for _crit leads to critical angles that are about twice previous predictions. It is shown that the present expression gives good agreement with the numerical results presented here, as well as with other numerical and experimental results. It is also consistent with atmospheric observations.     

Modelling of high amplitude internal waves integrating the primitive (Navier–Stokes) equations

In this paper we use an industrial Navier–Stokes (NS) solver to model high amplitude internal waves. The model simulates a fluid with a shallow upper layer with linear stratification and a deep lower layer with constant density, relevant to conditions in the ocean at several locations. Waves are generated by trapping a volume of light water behind a gate in one end of the numerical wave tank. The velocity and vorticity fields predicted by the model agree well with experiment. The high amplitude waves produced by the NS solver experience an upper bound on the velocity and a broadening in agreement with experiment. These effects have not previously been captured by theoretical models.     

The SWAN model used to study wave evolution in a flume

The SWAN numerical model is used to model the evolution of JONSWAP wave spectra and hence the significant wave height of waves in a tank. Comparison with experiment has shown that modelling triad interactions in the numerical model leads to too low predictions of spectra and significant wave height and should therefore be excluded. The modelling of the breaking constant was also investigated, by looking at the use of a constant breaking constant, Nelson formula, and Goda formula (added into SWAN for this study). Using a constant value of 0.78 within SWAN gave the best comparison between theory and experiment.     

Deep North Atlantic freshening simulated in a coupled climate model

The observed recent freshening trend in the deep North Atlantic and the Labrador Sea is investigated in three forced ensembles and a long control simulations using the HadCM3 coupled ocean–atmosphere–sea-ice climate model. The 40 yr freshening trend during the late half of the 20th century is captured in the all forcings ensemble that applies all major external (natural and anthropogenic) forcing factors. Each ensemble has four members with different initial conditions taking from the control run at a 100 yr interval. No similar freshening trend is found in each of the four corresponding periods of the control simulation. However, there are five large freshening events in a 1640 yr period of the control run, each following a sudden salinity increase. A process analysis revealed that the increase in salinity in the Labrador Sea is closely linked to deep convections while the following freshening trend is accompanied by a period of very weak convective activities.The fact that none of the five large freshening events appears in the four corresponding periods following the initial conditions of the four members of the all forcings ensemble suggest that external forcings may have contributed to triggering the events. Further analyses of two other ensemble simulations (natural forcings only and anthropogenic forcings only) have shown that natural rather than anthropogenic factors are responsible. Based on our model results, we can not attribute the simulated freshening to anthropogenic climate change.     

Moon: Central peak heights and crater origins

The heights of central peaks in lunar craters are directly proportional to crater diameters, implying that peak height is a function of crater-forming energy. A similar relationship exists for terrestrial meteorite and TNT craters whose uplifts are of rebound origin. A rebound origin for lunar central peaks implies an impact origin for central peak craters. Correlation of peak heights and crater depths provides direct evidence for lava filling of crater floors.     

Development and Implementation of a Bayesian-based Aquifer Vulnerability Assessment in Florida

The Florida Aquifer Vulnerability Assessment (FAVA) was designed to provide a tool for environmental, regulatory, resource management, and planning professionals to facilitate protection of groundwater resources from surface sources of contamination. The FAVA project implements weights-of-evidence (WofE), a data-driven, Bayesian-probabilistic model to generate a series of maps reflecting relative aquifer vulnerability of Florida’s principal aquifer systems. The vulnerability assessment process, from project design to map implementation is described herein in reference to the Floridan aquifer system (FAS). The WofE model calculates weighted relationships between hydrogeologic data layers that influence aquifer vulnerability and ambient groundwater parameters in wells that reflect relative degrees of vulnerability. Statewide model input data layers (evidential themes) include soil hydraulic conductivity, density of karst features, thickness of aquifer confinement, and hydraulic head difference between the FAS and the watertable. Wells with median dissolved nitrogen concentrations exceeding statistically established thresholds serve as training points in the WofE model. The resulting vulnerability map (response theme) reflects classified posterior probabilities based on spatial relationships between the evidential themes and training points. The response theme is subjected to extensive sensitivity and validation testing. Among the model validation techniques is calculation of a response theme based on a different water-quality indicator of relative recharge or vulnerability: dissolved oxygen. Successful implementation of the FAVA maps was facilitated by the overall project design, which included a needs assessment and iterative technical advisory committee input and review. Ongoing programs to protect Florida’s springsheds have led to development of larger-scale WofE-based vulnerability assessments. Additional applications of the maps include land-use planning amendments and prioritization of land purchases to protect groundwater resources.