Two-dimensional numerical modeling of dam-break flows over natural terrain using a central explicit scheme

A two-dimensional (2D) numerical model has been developed to solve shallow water equations for simulation of dam-break flows. The spatial derivatives are discretized using a well-balanced explicit central upwind conservative scheme. The scheme is Riemann solver free and guarantees the positivity of the flow depth over complex topography if the Courant number is kept less than 0.25. The time integration is performed by Euler’s scheme. The model is verified against analytical results for water surface elevation and discharge for three benchmark test cases. A good agreement between analytical solutions and computed results is observed. The property of well-balancing in still water over an uneven bottom is also confirmed. The model is then validated by simulating a laboratory experiment in which a dam break flow propagates over a triangular obstacle. The model performance was found to be satisfactory. A dam break laboratory experimental test case on a frictionless horizontal bottom is also simulated for 2D validation of the model, and good agreement between simulation and the experimental data is observed. The suitability of the proposed model for real life applications is demonstrated by simulating the Malpasset dam-break event, which occurred in 1959 in France. The computed arrival time of the flood wave front and the maximum flow depths at various observation points matched well with the measurements on a 1/400 scale physical model. The overall performance indicates that this model can be applied for simulation of dam-break waves in real life cases.     

Fractionation trends of basalt magmas in lava flows

Chemical compositions of schlieren in basalt flows are compared with those of the host rocks for tracing the fractionation trends of basalt magmas under extrusive conditions. In the Warner high-alumina basalt of California and in the tholeiite of Hawaii and Japan, total iron increases markedly from the host rock to the schlieren whileSiO ₂ is nearly constant. In the high-alumina basalt of Huzi Volcano and in the tholeiite near Catania, Italy, total iron is nearly constant during fractionation whileSiO ₂ increases. In basalts of the hypersthenic rock series or calc-alkali rock series from California, total iron is also nearly constant whileSiO ₂ increases. The difference in fractionation trend in these flows is attributable to the difference of the state of oxidation of iron in the original magmas. Oxygen partial pressure of the magmas would not be maintained constant during the fractionation of extrusive bodies.     

Processes of dike-break induced flows:A combined experimental and numerical model study

Dike breaking is a disaster that could cause extensive damage. It could lead to flood flows outside the dike and induce water level fluctuations in the main channel. Numerical models are increasingly used to simulate flood flows due to dike-break, because direct observations from field surveys and physical models are rather limited. Existing knowledge concerning dam-break flows cannot be applied directly to dike-break flows because the effect of channel discharge cannot be neglected in the latter. In this study,physical experiments are done in a large laboratory flume to simulate the process of dike-break induced flood wave propagation in the floodplain and flow fluctuations in the main channel. The variations of water levels and velocities are measured and recorded using an array of pressure sensors and two acoustic Doppler velocimetry devices. A numerical model has been set up according to the experimental layout. The experiments have high repeatability and the numerical model predictions agree closely with the physical model data. The experimental results provide reliable information for improving the understanding of dike-break flow dynamics and for the verification of numerical models.     

A case study of sub-basalt imaging in land region covered with basalt flows

In this study, a set of 20 2D seismic lines, acquired over the Golan Heights basaltic plateau, was processed and analysed. Although the data were acquired and processed by standard techniques, in some cases good-quality seismic images were obtained under several hundred metres of basalts. We describe how the seismic characteristics of the top basalt layer were defined and show the effect of the numerous widespread volcanic sources on the quality of the final images. The new data reveal the first images of the sedimentary sequence under the basalt flows, and indicate that strands of the Dead Sea Transform extend into this area. The entire region was found to be very deformed. Several attractive traps for hydrocarbon exploration were also identified on the output sections.     

Bubble growth in rhyolitic melts: experimental and numerical investigation

 Bubble growth controlled by mass transfer of water from hydrated rhyolitic melts at high pressures and temperatures was studied experimentally and simulated numerically. Rhyolitic melts were hydrated at 150 MPa, 780–850  °C to uniform water content of 5.5–5.3 wt%. The pressure was then dropped and held constant at 15–145 MPa. Upon the drop bubbles nucleated and were allowed to grow for various periods of time before final, rapid quenching of the samples. The size and number density of bubbles in the quenched glasses were recorded. Where number densities were low and run duration short, bubble sizes were in accord with the growth model of Scriven (1959) for solitary bubbles. However, most results did not fit this simple model because of interaction between neighboring bubbles. Hence, the growth model of Proussevitch et al. (1993), which accounts for finite separation between bubbles, was further developed and used to simulate bubble growth. The good agreement between experimental data, numerical simulation, and analytical solutions enables accurate and reliable examination of bubble growth from a limited volume of supersaturated melt. At modest supersaturations bubble growth in hydrated silicic melts (3–6 wt% water, viscosity 10⁴–10⁶ Pa·s) is diffusion controlled. Water diffusion is fast enough to maintain steady-state concentration gradient in the melt. Viscous resistance is important only at the very early stage of growth (t<1 s). Under the above conditions growth is nearly parabolic, R²=2Dtρ_m(C₀–C_f)/ρ_g until the bubble approaches its final size. In melts with low water content, viscosity is higher and maintains pressure gradients in the melt. Growth may be delayed for longer times, comparable to time scales of melt ascent during eruptions. At high levels of supersaturation, advection of hydrated melt towards the growing bubble becomes significant. Our results indicate that equilibrium degassing is a good approximation for modeling vesiculation in melts with high water concentrations (C₀>3 wt%) in the region above the nucleation level. When the melt accelerates and water content decreases, equilibrium can no longer be maintained between bubbles and melt. Supersaturation develops in melt pockets away from bubbles and new bubbles may nucleate. Further acceleration and increase in viscosity cause buildup of internal pressure in the bubbles and may eventually lead to fragmentation of the melt. Received: 19 June 1995 / Accepted: 27 December 1995     

Instability of planetary flows using Riemann curvature: a numerical study

ABSTRACT

The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnold (Ann. Inst. Fourier 1966, 16, 319) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.     

Imaging and regional distribution of basalt flows in the Faeroe-Shetland Basin

We demonstrate that the use of long-offset seismic data allows wide-angle reflections and diving waves to be recorded, and that these can be used in conjunction with prestack depth migrations to constrain and to image the base of the basalt flows and the underlying structure in the Faeroe-Shetland Basin. Crustal velocity models are built first by inverting the traveltimes of the recorded reflections and diving waves using ray-tracing methods. Finer details of the velocity structure can then be refined by analysis of the amplitudes and waveforms of the arrivals. We show that prestack depth migration of selected wide-angle arrivals of known origin, such as the base-basalt reflection, using the crustal velocity model, allows us to build a composite image of the structure down to the pre-rift basement. This has the advantage that the wide-angle first-arriving energy must be primary, and not from one of the many multiples or mode-converted phases that plague near-offset seismic data. This allows us to ‘tag’ these primary arrivals with confidence and then to identify the same arrivals on higher-resolution prestack migrations that include data from all offsets. Examples are drawn from the Faeroe-Shetland Basin, with a series of regional maps of the entire area showing the basalt depths and the thickness of the basalt flows and underlying sediment down to the top of the pre-rift basement. The maps show how the basalts thin to the southeast away from their presumed source west of the present Faeroe Islands, and also show the extent to which the structure of the pre-rift basement controls the considerable variations in sediment thickness between the basement and the cap formed by the overlying basalt flows.     

A multifractal model of crack coalescence in rocks

Geometric characteristics of fractal sets of cracks are investigated from the standpoint of their coalescence. A 1D computer model, in which a realistic character of forms of crack sets is achieved through the inducing of sets with the use of the multiplicative cascade procedure, is considered. The investigation is aimed at the determination of conditions of coalescence of cracks organized as a superposition of fractal subsets of a unified set of cracks. The process of crack coalescence is investigated for three different values of the coalescence criterion. The geometric characteristics of the sets of cracks that are necessary for the transition of the crack coalescence process into an avalanche-like stage are estimated.     

A comparison of cumulus parameterization schemes in a numerical weather prediction model for a monsoon rainfall event

In order to evaluate cumulus parameterization (CP) schemes for hydrological applications, the Pennsylvania State University–National Center for Atmospheric Research's fifth‐generation mesoscale model (MM5) was used to simulate a summer monsoon in east China. The performances of five CP schemes (Anthes–Kuo, Betts–Miller, Fritsch–Chappell, Kain–Fritsch, and Grell) were evaluated in terms of their ability to simulate amount of rainfall during the heavy, moderate, and light phases of the event. The Grell scheme was found to be the most robust, performing well at all rainfall intensity and spatial scales. The Betts–Miller scheme also performed well, particularly at larger scales, but its assumptions may make it inapplicable to non‐tropical environments and at smaller scales. The Kain–Fritsch scheme was the best at simulating moderate rainfall rates, and was found to be superior to the Fritsch–Chappell scheme on which it was based. The Anthes–Kuo scheme was found to underpredict precipitation consistently at the mesoscale. Simulation performance was found to improve when schemes that included downdrafts were used in conjunction with schemes that did not include downdrafts. Copyright © 2005 John Wiley & Sons, Ltd.     

Calibration of a numerical ionospheric model with EISCAT observations

A set of EISCAT UHF and VHP observations is used for calibrating a coupled fluid-kinetic model of the ionosphere. The data gathered in the period 1200–2400 UT on 24 March 1995 had various intervals of interest for such a calibration. The magnetospheric activity was very low during the afternoon, allowing for a proper examination of a case of quiet ionospheric conditions. The radars entered the auroral oval just after 1900 UT: a series of dynamic events probably associated with rapidly moving auroral arcs was observed until after 2200 UT. No attempts were made to model the dynamical behaviour during the 1900–2200 UT period. In contrast, the period 2200–2400 UT was characterised by quite steady precipitation: this latter period was then chosen for calibrating the model during precipitation events. The adjustment of the model on the four primary parameters observed by the radars (namely the electron concentration and temperature and the ion temperature and velocity) needed external inputs (solar fluxes and magnetic activity index) and the adjustments of a neutral atmospheric model in order to reach a good agreement. It is shown that for the quiet ionosphere, only slight adjustments of the neutral atmosphere models are needed. In contrast, adjusting the observations during the precipitation event requires strong departures from the model, both for the atomic oxygen and hydrogen. However, it is argued that this could well be the result of inadequately representing the vibrational states of N₂ during precipitation events, and that these factors have to be considered only as ad hoc corrections.     

A numerical model for the dynamics of pyroclastic flows at Galeras Volcano,Colombia

This paper presents a two-dimensional model for dilute pyroclastic flow dynamics that uses the compressible Navier–Stokes equation coupled with the Diffusion–Convection equation to take into account sedimentation. The model is applied to one of the slopes of Galeras Volcano to show: (1) the temperature evolution with the time; (2) dynamic pressure change; and (3) particle concentration along the computer domain from the eruption to the impact with a topographic barrier located more than 16 km from the source. Two initial solid volumetric fractions are modeled. For both cases, some of the structures located more distant than 10 km could survive, but in all cases the flow remains deadly. This paper shows that a dynamical model of pyroclastic flows can be implemented using personal computers.     

A comparison of numerical simulations of eddy generation performed with a two- and a three-layer quasi-geostrophic model of oceanic mesoscale eddies

Abstract

The generation of eddies by a large-scale flow over mesoscale topography is studied with the help of two- and three-layer nonlinear quasi-geostrophic models of the open ocean. The equations are integrated forward in time with no eddies present initially. For a given time, the displacement of the interface between layers two and three (ζ) tends to a well-defined limit (function of the horizontal spatial coordinates) as ρ ₃ - ρ ₂ → 0 (ρ_r is the density of layer r). Even for values of α[= (ρ ₃ - ρ ₂)/(ρ ₂ - ρ ₁)] ^as small as 0.01 the potential energy due to ζ is not negligible and it can reach, in some cases, a considerable fraction of the total eddy energy.     

Assessing a numerical cellular braided‐stream model with a physical model

A. B. Murray and C. Paola (1994, Nature, vol. 371, pp. 54–57; 1997, Earth Surface Processes and Landforms, vol. 22, pp. 1001–1025) proposed a cellular model for braided river dynamics as an exploratory device for investigating the conditions necessary for the occurrence of braiding. The model reproduces a number of the general morphological and dynamic features of braided rivers in a simplified form. Here we test the representation of braided channel morphodynamics in the Murray–Paola model against the known characteristics (mainly from a sequence of high resolution digital elevation models) of a physical model of a braided stream. The overall aim is to further the goals of the exploratory modelling approach by first investigating the capabilities and limitations of the existing model and then by proposing modifications and alternative approaches to modelling of the essential features of braiding. The model confirms the general inferences of Murray and Paola (1997) about model performance. However, the modelled evolution shows little resemblance to the real evolution of the small‐scale laboratory river, although this depends to some extent on the coarseness of the grid used in the model relative to the scale of the topography. The model does not reproduce the bar‐scale topography and dynamics even when the grid scale and amplitude of topography are adapted to be equivalent to the original Murray–Paola results. Strong dependence of the modelled processes on local bed slopes and the tendency for the model to adopt its own intrinsic scale, rather than adapt to the scale of the pre‐existing topography, appear to be the main causes of the differences between numerical model results and the physical model morphology and dynamics. The model performance can be improved by modification of the model equations to more closely represent the water surface but as an exploratory approach hierarchical modelling promises greater success in overcoming the identified shortcomings. Copyright © 2005 John Wiley & Sons, Ltd.     

Topographic stress and rock fracture: a two‐dimensional numerical model for arbitrary topography and preliminary comparison with borehole observations

Theoretical calculations indicate that elastic stresses induced by surface topography may be large enough in some landscapes to fracture rocks, which in turn could influence slope stability, erosion rates, and bedrock hydrologic properties. These calculations typically have involved idealized topographic profiles, with few direct comparisons of predicted topographic stresses and observed fractures at specific field sites. We use a numerical model to calculate the stresses induced by measured topographic profiles and compare the calculated stress field with fractures observed in shallow boreholes. The model uses a boundary element method to calculate the stress distribution beneath an arbitrary topographic profile in the presence of ambient tectonic stress. When applied to a topographic profile across the Susquehanna Shale Hills Critical Zone Observatory in central Pennsylvania, the model predicts where shear fractures would occur based on a Mohr–Coulomb criterion, with considerable differences in profiles of stresses with depth beneath ridgetops and valley floors. We calculate the minimum cohesion required to prevent shear failure, C_min, as a proxy for the potential for fracturing or reactivation of existing fractures. We compare depth profiles of C_min with structural analyses of image logs from four boreholes located on the valley floor, and find that fracture abundance declines sharply with depth in the uppermost 15 m of the bedrock, consistent with the modeled profile of C_min. In contrast, C_min increases with depth at comparable depths below ridgetops, suggesting that ridgetop fracture abundance patterns may differ if topographic stresses are indeed important. Thus, the present results are consistent with the hypothesis that topography can influence subsurface rock fracture patterns and provide a basis for further observational tests. Copyright © 2014 John Wiley & Sons, Ltd.     

A numerical study of rotating annulus flows using a modified Galerkin method

Summary Physical phenomena fundamental to rotating, baroclinically driven flows are studied with reference to results of numerical simulation of rotating annulus flows, using a modified Galerkin Model. Both local and global effects of sources, sinks, and transports of heat and momentum are discussed. A convenient energy exchange diagram reveals detailed information that is used to analyze nonlinear equilibration and amplitude vacillation of quasi-geostrophic baroclinic eddies. Transient inertial oscillations, sidewall boundary layers, and internal boundary layers are also discussed.A detailed study of symmetric flows is made, eleven of which are tested numerically for stability with respect to three-dimensional disturbances of a given zonal wave number. Two of the four unstable cases are integrated to a numerical steady state with finite-amplitude, quasi-geostrophic baroclinic waves. With the rigid-lid geometry assumed, the average zonal velocity is zero, resulting in zero phase velocity of the waves. The structure of the thermal wave is nearly coherent in the vertical. These numerical results are consistent with laboratory observations.The eddy flow is quasi-geostrophic except in horizontal boundary layers, where the flow is driven toward low pressure. A small cross-isotherm advection is sufficient to maintain the temperature wave against diffusion and vertical advection. The eddy flow adjusts spontaneously toward the form of the fastest growing or slowest decaying disturbance representable by the truncated space resolution. The eddy flow feeds energy into the mean zonal flow in barotropic-type interactions reflected mainly by the familiar tilted trough. During equilibration, the eddy flow alters the mean zonal flow in such a way that eddy energy sources are reduced relative to energy sinks. However, this adjustment is small compared to the change of total flow, which reflects a relatively large change of eddy amplitude. This suggests that small errors in the mean zonal flow representation can lead to relatively large errors in total flow representation.In most flows studied the kinetic energy dissipation is concentrated in thin boundary layers. In spite of this thinness, the basically laminar character of these dissipative boundary layers allows accurate and economical numerical simulation through the use of characteristic functions, which is a natural refinernent of the basic Galerkin method used. (In this prototype study, only moderately characteristic functions are used, thus sacrificing numerical economy while simplifying the programming.) Similarly, the generation of potential energy, which is transformed into the kinetic energy of the flow, is accurately simulated. In most cases studied, this generation is also concentrated in thin boundary layers where thermal energy is extracted from cold fluid and added to warm fluid.Contribution number 76 of the Geophysical Fluid Dynamics Institute, Florida State University, USA.     

A lattice Boltzmann model coupled with a Large Eddy Simulation model for flows around a groyne

This present paper proposes a two-dimensional lattice Boltzmann model coupled with a Large Eddy Simulation (LES) model and applies it to flows around a non-submerged groyne in a channel. The LES of shallow water equations is efficiently performed using the Lattice Boltzmann Method (LBM) and the turbulence can be taken into account in conjunction with the Smagorinsky Sub-Grid Stress (SGS) model. The bounce-back scheme of the non-equilibrium part of the distribution function is used to determine the unknown distribution functions at inflow boundary, the zero gradient of the distribution function is set normal to outflow boundary to obtain the unknown distribution functions here and the bounce-back scheme, which states that an incoming particle towards the boundary is bounced back into fluid, is applied to the solid wall to ensure non-slip boundary conditions. The initial flow field is defined firstly and then is used to calculate the local equilibrium distributions as initial conditions of the distribution functions. These coupled models successfully predict the flow characteristics, such as circulating flow, velocity and water depth distributions. The comparisons between the simulated results and the experimental data show that the model scheme has the capacity to solve the complex flows in shallow water with reasonable accuracy and reliability.     

Analysis of karst aquifer spring flows with a gray system decomposition model

There are approximately 470,000 km(2) of karst aquifers that feed many large springs in North China. Turbulent flow often exists in these karst aquifers, which means that the classical ground water model based on Darcy's law cannot be applied here. Ground water data are rare for these aquifers. As a consequence, it is difficult to quantitatively investigate ground water flow in these karst systems. The purpose of this study is to develop a parsimonious model that predicts karst spring discharge using gray system theory. In this theory, a white color denotes a system that is completely characterized and a black color represents a system that is totally unknown. A gray system thus describes a complex system whose characteristics are only partially known or known with uncertainty. Using this theory, we investigated the karst spring discharge time series over different time scales. First, we identified three specific components of spring discharge: the long-term trend, periodic variation, and random fluctuation. We then used the gray system model to simulate the long-term trend and obtain periodic variation and random fluctuation components. Subsequently, we developed a predictive model for karst spring discharge. Application of the model to Liulin Springs, a representative example of karst springs in northern China, shows that the model performs well. The predicted results suggest that the Liulin Springs discharge will likely decrease over time, with small fluctuations.     

Spatial variability of soils developing on basalt flows in the Potrillo volcanic field,southern New Mexico: prelude to a chronosequence study

If the systematic spatial variability of soils in a chronosequence is identified and accounted for, the accuracy of quantitative data derived from soil chronosequence studies will be increased. A sample design using landscape positions with minimal variability could result in more accurate chronofunctions from these studies. Four basalt flows in the Potrillo volcanic field, southern New Mexico, with ages ranging between 20 ka and 260 ka (⁴⁰Ar/³⁹Ar and/or cosmogenic ³He methods) provide a sound basis for a soil chronosequence study. Basalt flow surface relief in the Potrillos reduces with time as depressions fill with basalt rubble and aeolian dust. Soil variability is primarily a function of landscape position with respect to ridges and swales in the original basalt flow topography. Soils developing over original topographic lows (swale soils) form primarily in aeolian dust, have larger amounts of total carbonate and soluble salts, and display greater variability than soils developing over original topographic highs (ridge soils). It is thus concluded that ridge soils, which have minimal variability, should be employed for a soil chronosequence study of basalt surfaces in the Potrillo volcanic field. The spatial variability of swale soils results in part from the significant hydrologic variability of low-lying landscape positions. Depth profiles of chloride concentrations suggest that hydrologic variability systematically correlates with the size and shape of depressions in which soils are forming. The infilling of depressions with aeolian material results in increasingly arid hydrologic conditions both by increasing the volume of aeolian material that is being drained and by reducing the catchment area for runoff into the depression. Depressions fill at different rates, however, depending on their size, shape and catchment area. Small, narrow depressions fill quickly, and their associated soils form under more arid conditions and have stronger development than soils in large depressions. Therefore, a number of geomorphic surfaces of varying age may develop on a single isochronous basalt flow. Each of these surfaces will have unique hydrologic characteristics and consequently different degrees of soil development. The pre-burial high water flux evident in depressions suggests that basalt flows may play an important role in aquifer recharge in this area of New Mexico. Copyright © 1999 John Wiley & Sons, Ltd.     

Evaluation of a gravel transport sensor for bed load measurements in natural flows

A recent acoustic instrument （Gravel Transport Sensor, GTS） was tested for predicting sediment transport rate （bed load rate） in gravel bed streams. The GTS operation is based on the particle collision theory of submerged obstacles in fluids. When particles collide with the GTS cylinder their momentum is recorded in the form of ping rates. The GTS is attractive for further consideration here because of its potential to provide continuous unattended local bed load measurements, especially in areas found in streams that access may be difficult under extreme conditions. Laboratory experiments coupled with numerical simulations for the same flow conditions were performed in order to determine the conditions under which particles of different size will hit the GTS cylinder and be able to register a ping rate. The GTS was able to detect the number of particles with diameter in the range of 15.9 to 25.4 mm, with reasonable accuracy, if the applied Shields effective stress τ＊e = τ＊ - τ＊cr was in the range of 0.006 to 0.015. A drawback of the tested prototype GTS, however, was that it exerted increased resistance on the incoming particles. The added drag effects increased the overall resistance that was exerted by the flow on particles and thus increased the likelihood that particles will rest in the ambient region of the cylinder instead of hitting it. Numerical simulation of the flow around the GTS cylinder revealed that changing the prototype geometry from cylindrical to ellipsoid or rhomboid will increase the likelihood of the particles hitting the instrument under the same flow conditions failed by the original tested GTS cylinder.     

A comparison between experimental and numerical investigations of the motion of the water surface in a model surge tank

This paper describes an investigation into the motion of the water surface in a simple model surge tank, and the relevant factors governing its behaviour. The oscillation of the free water surface is an unsteady flow problem, which is amenable to a mathematical solution using a finite difference step-by-step integration procedure. For comparison, two such methods are presented: (i) a simple initial value method and (ii) a predictor-corrector technique. Computer programs have been developed linked to a graph plotter to give a visual presentation of the numerical solutions together with the experimental results of the damped oscillation of the water surface in the model surge tank.