Lava flow hazard at Nyiragongo volcano,D.R.C.

The 2002 eruption of Nyiragongo volcano constitutes the most outstanding case ever of lava flow in a big town. It also represents one of the very rare cases of direct casualties from lava flows, which had high velocities of up to tens of kilometer per hour. As in the 1977 eruption, which is the only other eccentric eruption of the volcano in more than 100 years, lava flows were emitted from several vents along a N–S system of fractures extending for more than 10 km, from which they propagated mostly towards Lake Kivu and Goma, a town of about 500,000 inhabitants. We assessed the lava flow hazard on the entire volcano and in the towns of Goma (D.R.C.) and Gisenyi (Rwanda) through numerical simulations of probable lava flow paths. Lava flow paths are computed based on the steepest descent principle, modified by stochastically perturbing the topography to take into account the capability of lava flows to override topographic obstacles, fill topographic depressions, and spread over the topography. Code calibration and the definition of the expected lava flow length and vent opening probability distributions were done based on the 1977 and 2002 eruptions. The final lava flow hazard map shows that the eastern sector of Goma devastated in 2002 represents the area of highest hazard on the flanks of the volcano. The second highest hazard sector in Goma is the area of propagation of the western lava flow in 2002. The town of Gisenyi is subject to moderate to high hazard due to its proximity to the alignment of fractures active in 1977 and 2002. In a companion paper (Chirico et al., Bull Volcanol, in this issue, 2008) we use numerical simulations to investigate the possibility of reducing lava flow hazard through the construction of protective barriers, and formulate a proposal for the future development of the town of Goma.     

Coupled groundwater flow and transport: 1. Verification of variable density flow and transport models

This work examines variable density flow and corresponding solute transport in groundwater systems. Fluid dynamics of salty solutions with significant density variations are of increasing interest in many problems of subsurface hydrology. The mathematical model comprises a set of non-linear, coupled, partial differential equations to be solved for pressure/hydraulic head and mass fraction/concentration of the solute component. The governing equations and underlying assumptions are developed and discussed. The equation of solute mass conservation is formulated in terms of mass fraction and mass concentration. Different levels of the approximation of density variations in the mass balance equations are used for convection problems (e.g. the Boussinesq approximation and its extension, fully density approximation). The impact of these simplifications is studied by use of numerical modelling.Numerical models for nonlinear problems, such as density-driven convection, must be carefully verified in a particular series of tests. Standard benchmarks for proving variable density flow models are the Henry, Elder, and salt dome (HYDROCOIN level 1 case 5) problems. We studied these benchmarks using two finite element simulators - ROCKFLOW, which was developed at the Institute of Fluid Mechanics and Computer Applications in Civil Engineering and FEFLOW, which was developed at the Institute for Water Resources Planning and Systems Research Ltd. Although both simulators are based on the Galerkin finite element method, they differ in many approximation details such as temporal discretization (Crank-Nicolson vs predictor-corrector schemes), spatial discretization (triangular and quadrilateral elements), finite element basis functions (linear, bilinear, biquadratic), iteration schemes (Newton, Picard) and solvers (direct, iterative). The numerical analysis illustrates discretization effects and defects arising from the different levels of the density of approximation. We contribute new results for the salt dome problem, for which inconsistent findings exist in literature. Applications of the verified numerical models to more complex problems, such as thermohaline and three-dimensional convection systems, will be presented in the second part of this paper.     

Directions of preferential flow in a hillslope soil, 1. Quasi‐steady flow

Preferred infiltration is mainly perceived as vertically down whereas subsurface storm flow is thought to occur parallel to slopes. The transition from vertical to lateral flow in a layered hillslope soil is the focus of the contribution. Transient flow is assumed to move as a wetting front. Three time‐domain reflectometry (TDR) wave‐guides, each 0·15 m long, were mounted in the shape of a truncated tetrahedron with its peak pointing down. Each wave‐guide focuses the front velocity along its axis. The three front‐velocity vectors are decomposed into their x, y and z components, which are then assembled to the resultant velocity vector. The volume density flux of preferred flow is the product of the front velocity and the mobile water content. The latter is the amplitude of transient soil moisture measured with each wave‐guide. The resultant vector of the volume flux density is computed similarly to the velocity vector. The experimental approach allows for the rapid assessment of transient flows without relying on the variation of water potentials. The experiments indicate that the directions of the resultant vectors of velocity and volume flux density can be estimated if the moisture variations of the three TDR wave‐guides are strongly correlated during the passing of the wetting front. Copyright © 2004 John Wiley & Sons, Ltd.     

Sensitivity analysis of two-dimensional steady-state aquifer flow equations. Implications for groundwater flow model calibration and validation

This paper presents the analytical properties of the sensitivity of the two-dimensional, steady-state groundwater flow equation to the flow parameters and to the boundary conditions, based on the perturbation approach. These analytical properties are used to provide guidelines for model design, model calibration and monitoring network design. The sensitivity patterns are shown to depend on the nature of both the perturbed parameter and the variable investigated. Indeed, the sensitivity of the hydraulic head to the hydraulic conductivity extends mainly in the flow direction, while the sensitivity to the recharge spreads radially. Besides, the sensitivity of the flow longitudinal velocity to the hydraulic conductivity propagates in both the longitudinal and transverse directions, whereas the sensitivity of the flow transverse velocity propagates in the diagonal directions to the flow. The analytical results are confirmed by application examples on idealized and real-world simulations. These analytical findings allow some general rules to be established for model design, model calibration and monitoring network design. In particular, the optimal location of measurement points depends on the nature of the variable of interest. Measurement network design thus proves to be problem-dependent. Moreover, adequate monitoring well network design may allow to discriminate between the possible sources of error.     

Sensitivity analysis of 2D steady-state shallow water flow. Application to free surface flow model calibration

This paper presents the analytical properties of the solutions of the sensitivity equations for steady-state, two-dimensional shallow water flow. These analytical properties are used to provide guidelines for model calibration and validation. The sensitivity of the water depth/level and that of the longitudinal unit discharge are shown to contain redundant information. Under subcritical conditions, the sensitivities of the flow variables are shown to obey an anisotropic elliptic equation. The main directions of the contour lines for water depth and the longitudinal unit discharge sensitivity are parallel and perpendicular to the flow, while they are diagonal to the flow for the transverse unit discharge sensitivity. Moreover, the sensitivity for all three variables extends farther in the transverse direction than in the longitudinal direction, the anisotropy ratio being a function of the sole Froude number. For supercritical flow, the sensitivity obeys an anisotropic hyperbolic equation. These findings are confirmed by application examples on idealized and real-world simulations. The sensitivities to the geometry, friction coefficient or model boundary conditions are shown to behave in different ways, thus providing different types of information for model calibration and validation.     

Heat flow map of the European part of the U.S.S.R.

A heat flow isoline map is presented. Low and relatively constant heat flow has been observed in the old shield areas of the East European Platform (25–40 mW/m²). Increased heat flow (>50 mW/m²) has been found in the Dniepr-Donetz depression. The area south of the East European Platform is characterized by highly variable heat flow (55–100 mW/m²). Some geophysical implications are discussed.     

Lava flow hazard and risk at Mt. Cameroon volcano

Mt. Cameroon is one of the most active effusive volcanoes in Africa. About 500,000 people living or working around its fertile flanks are subject to significant threat from lava flow inundation. Lava flow hazard and risk were assessed by simulating probable lava flow paths using the DOWNFLOW code. The vent opening probability density function and lava flow length distribution were determined on the basis of available data from past eruptions at Mt. Cameroon volcano. Code calibration was performed through comparison with real lava flow paths. The topographic basis for simulations was the 90-m resolution SRTM DEM. Simulated lava flows from about 80,000 possible vents were used to produce a detailed lava flow hazard map. The lava flow risk in the area was mapped by combining the hazard map with digitized infrastructures (i.e., human settlements and roads). Results show that the risk of lava flow inundation is greatest in the most inhabited coastal areas comprising the town of Limbe, which constitutes the center of Cameroon’s oil industry and an important commercial port. Buea, the second most important town in the area, has a much lower risk although it is significantly closer to the summit of the volcano. Non-negligible risk characterizes many villages and most roads in the area surrounding the volcano. In addition to the conventional risk mapping described above, we also present (1) two reversed risk maps (one for buildings and one for roads), where each point on the volcano is classified according to the total damage expected as a consequence of vent opening at that point; (2) maps of the lava catchments for the two main towns of Limbe and Buea, illustrating the expected damage upon venting at any point in the catchment basin. The hazard and risk maps provided here represent valuable tools for both medium/long-term land-use planning and real-time volcanic risk management and decision making.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 6. Two-fluid-phase flow

This work is the sixth in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach for modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works, the limiting case of connected two-fluid-phase flow is considered. A constrained entropy inequality is developed based upon a set of primary restrictions. Formal approximations are introduced to deduce a general simplified entropy inequality (SEI). The SEI is used along with secondary restrictions and closure approximations consistent with the SEI to produce a general functional form of a two-phase-flow model. The general model is in turn simplified to yield a hierarchy of models by neglecting common curves and by neglecting both common curves and interfaces. The simplest case considered corresponds to a traditional two-phase-flow model. The more sophisticated models including interfaces and common curves are more physically realistic than traditional models. All models in the hierarchy are posed in terms of precisely defined variables that allow for a rigorous connection with the microscale. The explicit nature of the restrictions and approximations used in developing this hierarchy of models provides a clear means to both understand the limitations of traditional models and to build upon this work to produce more realistic models.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 3. Single-fluid-phase flow

This work is the third in a series of papers on the thermodynamically constrained averaging theory (TCAT) approach to modeling flow and transport phenomena in multiscale porous medium systems. Building upon the general TCAT framework and the mathematical foundation presented in previous works in this series, we demonstrate the TCAT approach for the case of single-fluid-phase flow. The formulated model is based upon conservation equations for mass, momentum, and energy and a general entropy inequality constraint, which is developed to guide model closure. A specific example of a closed model is derived under limiting assumptions using a linearization approach and these results are compared and contrasted with the traditional single-phase-flow model. Potential extensions to this work are discussed. Specific advancements in this work beyond previous averaging theory approaches to single-phase flow include use of macroscale thermodynamics that is averaged from the microscale, the use of derived equilibrium conditions to guide a flux–force pair approach to simplification, use of a general Lagrange multiplier approach to connect conservation equation constraints to the entropy inequality, and a focus on producing complete, closed models that are solvable.     

Resistance to flow in rough supercritical sheet flow

Shallow water depths on steep slopes of as much as fifty per cent can be measured easily by weighing a light flume and the water it contains. Because water accelerates along the flume, a good approximation of the steady state depth is obtained when the recording balance is fixed to its bottom end. From the unit discharge and the depth, and not from measurements of the surface velocity, the Darcy-Weisbach friction coefficient can be calculated. The present results show that this friction coefficient is larger in thin sheet flows than that calculated from the equation for rough turbulent flow. This latter could fit at a Reynolds Number of 50,000. When the regime is laminar (Re < 2,440) the Darcy-Weisbach friction coefficient always exceeds the theoretical value of 96/Re. The great relative depth of standing and travelling waves could account for this discrepancy together with turbulence and wake formation around bottom grains. Herein it is assumed that a regime can prevail where a laminar superlayer glides over a turbulent sublayer in the vicinity of bottom grains, because the ratio of the surface velocity to the mean velocity can greatly exceed 1.5, especially on steep slopes. Until photographs of the streamlines are taken, no statement about flow regimes in supercritical sheet flow can be made.     

Soil pipe flow tracer experiments: 1. Connectivity and transport characteristics

Much debate has occurred in catchment hydrology regarding the connectivity of flow paths from upslope areas to catchment outlets. This study was conducted in two catchments, one with three upper branches, in a loess soil with a fragipan that fosters lateral flow and exhibits an extensive distribution of soil pipe collapse features. The study aimed to determine the connectivity of multiple soil pipe networks as well as determine pipe flow velocities during storm events. Fluorescein dye was injected directly into soil pipes at the upper most pipe collapse feature of four different hillslopes. Breakthrough curves (BTC) were determined by sampling multiple pipe collapse features downslope. The BTCs were used to determine the ‘average’ (centre of mass) and ‘maximum’ (first arrival) flow velocities. This study confirmed that these catchments contain individual continuous soil pipe networks that extend over 190 m and connect the upper most hillslopes areas with the catchment outlet. While the flow paths are continuous, the individual pipe networks consist of alternating reaches of subsurface flow through soil pipes and reaches of surface flow through gullies formed by pipe collapses. In addition, flow can be occurring both through the subsurface soil pipes simultaneous with surface flow generated by artesian flow from the soil pipes. The pipe flow velocities were as high as 0.3 m/s, which was in the range of streamflow velocities. These pipe flow velocities were also in the range of velocities observed in pinhole erosion tests suggesting that these large, mature soil pipes are still actively eroding. Copyright © 2015 John Wiley & Sons, Ltd.     

Aeolian processes across transverse dunes. I: Modelling the air flow

This paper discusses a two-dimensional second-order closure model simulating air flow and turbulence across transverse dunes. Input parameters are upwind wind speed, topography of the dune ridge and surface roughness distribution over the ridge. The most important output is the distribution of the friction velocity over the surface. This model is dynamically linked to a model that calculates sand transport rates and the resulting changes in elevation. The sand transport model is discussed in a separate paper. The simulated wind speeds resemble patterns observed during field experiments. Despite the increased wind speed over the crest, the friction velocity at the crest of a bare dune is reduced compared to the upstream value, because of the effect of stream line curvature on turbulence. These curvature effects explain why desert dunes can grow in height. In order to obtain realistic predictions of friction velocity it was essential to include equations for the turbulent variables in the model. In these equations streamline curvature is an important parameter. The main flaw of the model is that it cannot deal with flow separation and the resulting recirculation vortex. As a result, the increase of the wind speed and friction velocity after a steep dune or a slipface will be too close to the dune foot. In the sand transport model this was overcome by defining a separation zone. Copyright © 1999 John Wiley & Sons, Ltd.     

Thermodynamically constrained averaging theory approach for modeling flow and transport phenomena in porous medium systems: 7. Single-phase megascale flow models

This work is the seventh in a series that introduces and employs the thermodynamically constrained averaging theory (TCAT) for modeling flow and transport in multiscale porous medium systems. This paper expands the previous analyses in the series by developing models at a scale where spatial variations within the system are not considered. Thus the time variation of variables averaged over the entire system is modeled in relation to fluxes at the boundary of the system. This implementation of TCAT makes use of conservation equations for mass, momentum, and energy as well as an entropy balance. Additionally, classical irreversible thermodynamics is assumed to hold at the microscale and is averaged to the megascale, or system scale. The fact that the local equilibrium assumption does not apply at the megascale points to the importance of obtaining closure relations that account for the large-scale manifestation of small-scale variations. Example applications built on this foundation are suggested to stimulate future work.     

Stochastic analysis of multiphase flow in porous media: II. Numerical simulations

The first paper (Chang et al., 1995b) of this two-part series described the stochastic analysis using spectral/perturbation approach to analyze steady state two-phase (water and oil) flow in a, liquid-unsaturated, three fluid-phase porous medium. In this paper, the results between the numerical simulations and closed-form expressions obtained using the perturbation approach are compared. We present the solution to the one-dimensional, steady-state oil and water flow equations. The stochastic input processes are the spatially correlated logk where k is the intrinsic permeability and the soil retention parameter, . These solutions are subsequently used in the numerical simulations to estimate the statistical properties of the key output processes. The comparison between the results of the perturbation analysis and numerical simulations showed a good agreement between the two methods over a wide range of logk variability with three different combinations of input stochastic processes of logk and soil parameter . The results clearly demonstrated the importance of considering the spatial variability of key subsurface properties under a variety of physical scenarios. The variability of both capillary pressure and saturation is affected by the type of input stochastic process used to represent the spatial variability. The results also demonstrated the applicability of perturbation theory in predicting the system variability and defining effective fluid properties through the ergodic assumption.     

Lithic breccias in pyroclastic flow deposits on St. Kitts,West Indies

Lithic-rich breccias are described from within a sequence of young (2000–3000 yrs B.P.) scoria and ash flow deposits erupted from Mount Misery and an older pumice and ash flow deposit (ignimbrite) on St. Kitts. Cross sections constructed through pyroclastic flow fans in well-exposed sea cliffs 4–6 km from the vent show that the lithic breccias are lensoid deposits which seem to occur as channel-shaped accumulations (up to > 20 m thick and > 150 m wide) within flow units. The best-developed example infills a deeply incised channel cut into older flow units. The coarsest lithic breccias are clast supported and fines depleted and grade laterally and vertically through finer-grained, matrix-supported breccias into scoria and ash flow deposits. Coarse scoria-concentration zones mainly occur at the tops of scoria and ash flow units but also at the bases, and gas-segregation pipes are common. The lithic breccias are a type of body-concentration deposit as they pass laterally into normal scoria and ash flow deposits and, where best developed, clearly occur above a reversely graded basal shear zone or layer. Grain-size studies indicate the lithic breccias and parent flows are strongly fines depleted and were highly fluidized. We suggest this may be a feature of many Lesser Antillean pyroclastic flows because of increased turbulence-induced fluidization resulting from a high degree of surface roughness caused by the steep (up to 40 °) irregular slopes, densely vegetated sinuous gullies of the tropical volcanoes, and ingestion and ignition of large amounts of lush vegetation. Accumulation of batches of lithics concentrated in the highly fluidized flows began at the break in slope where flows moved from gullies across hydraulic jumps onto the outer coastal flanks. The accumulations of breccias continued to move and be channelled down the central parts of the flows. Initially, on crossing onto the lower slopes, some of these flows seem to have had very powerfully erosive, nondepositional heads, and in the extreme example a deep channel as long as 1–2 km may have cut through underlying flow units at least as far as the present coastline. Much of the overriding remainder of the flow then drained away laterally. Thin, fine-grained ash flow deposits may form a marginal overbank facies to the pyroclastic flow fans.     

Groundwater flow and implications for groundwater contamination north of Prewitt,New Mexico,U.S.A.

In the southern San Juan Basin, New Mexico, strata of Permian and younger age dip gently toward the center of the basin. Most previous investigators believed that recharge to these strata occurred by precipitation on the outcrops and groundwater flowed downdip to the north and northeast. Recent water-level measurements in an undeveloped part of the basin near Prewitt, New Mexico, show that groundwater at shallow depths in alluvium and bedrock flows southward, opposite to the dip direction, and toward a major ephemeral drainage in a strike valley. North of this area, groundwater in deep bedrock aquifers does appear to flow northward. This information suggests that there are two groundwater circulation patterns; a shallow one controlled by topography and a deeper one controlled by geologic structure.Significant amounts of recharge to sandstone aquifers by infiltration through outcrops is unlikely due to the near-vertical exposures on cliffs, the gentle dip of the strata, and small annual precipitation. Numerical model results suggest that recharge to bedrock aquifers may be from downward leakage via aquitards over large areas and leakage from narrow alluvial aquifers in the subcrop area. The recharge mechanism is controlled by the hydraulic conductivity of the strata.As the flow path is controlled by hydraulic conductivity contrasts, geologic structure, and topography, contamination movement from surface impoundments is likely to be difficult to predict without a thorough hydrogeological site investigation.     

Plume heat flow is much lower than CMB heat flow

Plumes rising from the core–mantle boundary (CMB) are often assumed to transport most, or all, of the heat conducted across the CMB. Here this assumption is explored using numerical convection models in idealized geometries that lead to a single plume under steady-state or near steady state conditions. Plume heat transport is calculated for different internal heating rates using two methods and compared to the CMB heat flux. For these conditions, it is found that the heat flux transported by plumes in the upper mantle is only a fraction of the core heat flux and, thus, core heat flow estimates derived from observed hotspots could be multiplied by a factor of several.