Search results for: shallow water equations

Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

Abstract:

We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: dam-break problems, finite volume method, run-up waves, shallow water flows, wet/dry interfaces

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Authors: Etsuo Morishita

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In this paper, we show shallow water in a tin box as an analogous simulation tool for high-speed aerodynamics education and research. It is customary that we use a water tank to create shallow water flow. While a flow in a water tank is not necessarily uniform and is sometimes wavy, we can visualize a clear supercritical flow even when we move a body manually in stationary water in a simple shallow tin box. We can visualize a blunt shock wave around a moving circular cylinder together with a shock pattern around a diamond airfoil. Another interesting analogous experiment is a hydrodynamic shock tube with water and tea. We observe the contact surface clearly due to color difference of the two liquids those are invisible in the real gas dynamics experiment. We first revisit the similarities between high-speed aerodynamics and shallow water hydraulics. Several educational and research experiments are then introduced for engineering students. Shallow water experiments in a tin box simulate properly the high-speed flows.

Keywords: aerodynamics compressible flow, gas dynamics, hydraulics, shock wave

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Authors: Shengjun Yan, Xuan Wang

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Water level changes in a shallow lake always introduce dramatic land pattern changes. To achieve sustainable ecosystem service, it is necessary to evaluate habitat quality dynamic and its spatio-temporal variation resulted from water level changes, which can provide a scientific basis for protection of biodiversity and planning of wetland ecological system. Landsat data in the spring was chosen to obtain landscape data at different times based on the high, moderate and low water level of Baiyangdian Shallow Lake. We used the InVEST to evaluate the habitat quality, habitat degradation, and habitat scarcity. The result showed that: 1) the water level of shallow lake changes from high to low lead to an obvious landscape pattern changes and habitat degradation, 2) the most change area occurred in northwestward and southwest of Baiyangdian Shallow Lake, which there was a 21 percent of suitable habitat and 42 percent of moderately suitable habitat lost. Our findings show that the changes of water level in the shallow lake would have a strong relationship with the habitat quality.

Keywords: habitat quality, habitat degradation, water level changes, shallow lake

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Authors: Sidrah Ahmed

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The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: finite difference schemes, Riemann problem, shallow water equations, temperature gradients

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Authors: Mohamed Elshobaki, Alessandro Valiani, Valerio Caleffi

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In this paper, we solve 1-D shallow water equation for sub-critical and super-critical water flow at junction. The water flow at junction has been studied for the last 50 years from the physical-hydraulic point of views and for numerical computations need more attention. For numerical simulation, we need to establish an inner boundary condition at the junction to avoid an oscillation which rise from the waves interactions at the junction. Indeed, we introduce a new boundary condition at the junction based on the mass conservation, total head, and the admissible wave relations between the flow parameters in the three branches to predict the water depths and discharges at the junction. These boundary conditions are valid for sub-critical flow and super-critical flow.

Keywords: numerical simulation, junction flow, sub-critical flow, super-critical flow

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Authors: Fazlul Karim, Esa Al-Islam

Abstract:

Many problems in oceanography and environmental sciences require the solution of shallow water equations on physical domains having curvilinear coastlines and abrupt changes of ocean depth near the shore. Finite-difference technique for the shallow water equations representing the boundary as stair step may give inaccurate results near the coastline where results are of greatest interest for various applications. This suggests the use of methods which are capable of incorporating the irregular boundary in coastal belts. At the same time, large velocity gradient is expected near the beach and islands as water depth vary abruptly near the coast. A nested numerical scheme with fine resolution is the best resort to enhance the numerical accuracy with the least grid numbers for the region of interests where the velocity changes rapidly and which is unnecessary for the away of the region. This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. In this paper, we develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.

Keywords: Indonesian tsunami of 2004, Boundary-fitted nested grid model, Southern Thailand, finite difference method

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Authors: Julia Zimmerman, Gaurav Savant

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This study aims to evaluate the efficacy of the U.S. Army Corp of Engineers’ River Analysis System (HEC-RAS) application to modeling the hydraulics of estuaries. HEC-RAS has been broadly used for a variety of riverine applications. However, it has not been widely applied to the study of circulation in estuaries. This report details the model development and validation of a combined 1D/2D unsteady flow hydraulic model using HEC-RAS for estuaries and they are associated with tidally influenced rivers. Two estuaries, Galveston Bay and Delaware Bay, were used as case studies. Galveston Bay, a bar-built, vertically mixed estuary, was modeled for the 2005 calendar year. Delaware Bay, a drowned river valley estuary, was modeled from October 22, 2019, to November 5, 2019. Water surface elevation was used to validate both models by comparing simulation results to NOAA’s Center for Operational Oceanographic Products and Services (CO-OPS) gauge data. Simulations were run using the Diffusion Wave Equations (DW), the Shallow Water Equations, Eulerian-Lagrangian Method (SWE-ELM), and the Shallow Water Equations Eulerian Method (SWE-EM) and compared for both accuracy and computational resources required. In general, the Diffusion Wave Equations results were found to be comparable to the two Shallow Water equations sets while requiring less computational power. The 1D/2D combined approach was valid for study areas within the 2D flow area, with the 1D flow serving mainly as an inflow boundary condition. Within the Delaware Bay estuary, the HEC-RAS DW model ran in 22 minutes and had an average R² value of 0.94 within the 2-D mesh. The Galveston Bay HEC-RAS DW ran in 6 hours and 47 minutes and had an average R² value of 0.83 within the 2-D mesh. The longer run time and lower R² for Galveston Bay can be attributed to the increased length of the time frame modeled and the greater complexity of the estuarine system. The models did not accurately capture tidal effects within the 1D flow area.

Keywords: Delaware bay, estuarine hydraulics, Galveston bay, HEC-RAS, one-dimensional modeling, two-dimensional modeling

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Authors: Abhishek Saha, Serene Tay, Gerard Pijcke

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The availability of high-resolution topography and rainfall information in urban areas has made it necessary to revise modeling approaches used for simulating flood risk assessments. Lidar derived elevation models that have 1m or lower resolutions are becoming widely accessible. The classical approaches of 1D-2D flow models where channel flow is simulated and coupled with a coarse resolution 2D overland flow models may not fully utilize the information provided by high-resolution data. In this context, a study was undertaken to compare three different modeling approaches to simulate flooding in an urban area. The first model used is the base model used is Sobek, which uses 1D model formulation together with hydrologic boundary conditions and couples with an overland flow model in 2D. The second model uses a full 2D model for the entire area with shallow water equations at the resolution of the digital elevation model (DEM). These models are compared against another shallow water equation solver in 2D, which uses a subgrid method for grid refinement. These models are simulated for different horizontal resolutions of DEM varying between 1m to 5m. The results show a significant difference in inundation extents and water levels for different DEMs. They are also sensitive to the different numerical models with the same physical parameters, such as friction. The study shows the importance of having reliable field observations of inundation extents and levels before a choice of model and data can be made for spatial flood risk assessments.

Keywords: flooding, DEM, shallow water equations, subgrid

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Authors: Alia Alghosoun, Ashraf Osman, Mohammed Seaid

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A coupled two-layer finite volume/finite element method was proposed for solving dam-break flow problem over deformable beds. The governing equations consist of the well-balanced two-layer shallow water equations for the water flow and a linear elastic model for the bed deformations. Deformations in the topography can be caused by a brutal localized force or simply by a class of sliding displacements on the bathymetry. This deformation in the bed is a source of perturbations, on the water surface generating water waves which propagate with different amplitudes and frequencies. Coupling conditions at the interface are also investigated in the current study and two mesh procedure is proposed for the transfer of information through the interface. In the present work a new procedure is implemented at the soil-water interface using the finite element and two-layer finite volume meshes with a conservative distribution of the forces at their intersections. The finite element method employs quadratic elements in an unstructured triangular mesh and the finite volume method uses the Rusanove to reconstruct the numerical fluxes. The numerical coupled method is highly efficient, accurate, well balanced, and it can handle complex geometries as well as rapidly varying flows. Numerical results are presented for several test examples of dam-break flows over deformable beds. Mesh convergence study is performed for both methods, the overall model provides new insight into the problems at minimal computational cost.

Keywords: dam-break flows, deformable beds, finite element method, finite volume method, hybrid techniques, linear elasticity, shallow water equations

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Authors: K. P. Mredula, D. C. Vakaskar

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The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc.

Keywords: multi-resolution, Haar Wavelet, partial differential equation, numerical methods

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Authors: Rabih Ghostine, Craig Kapfer, Viswanathan Kannan, Ibrahim Hoteit

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Urban flooding resulting from a sudden release of water due to dam-break or excessive rainfall is a serious threatening environment hazard, which causes loss of human life and large economic losses. Anticipating floods before they occur could minimize human and economic losses through the implementation of appropriate protection, provision, and rescue plans. This work reports on the numerical modelling of flash flood propagation in urban areas after an excessive rainfall event or dam-break. A two-dimensional (2D) depth-averaged shallow water model is used with a refined unstructured grid of triangles for representing the urban area topography. The 2D shallow water equations are solved using a second-order well-balanced discontinuous Galerkin scheme. Theoretical test case and three flood events are described to demonstrate the potential benefits of the scheme: (i) wetting and drying in a parabolic basin (ii) flash flood over a physical model of the urbanized Toce River valley in Italy; (iii) wave propagation on the Reyran river valley in consequence of the Malpasset dam-break in 1959 (France); and (iv) dam-break flood in October 1982 at the town of Sumacarcel (Spain). The capability of the scheme is also verified against alternative models. Computational results compare well with recorded data and show that the scheme is at least as efficient as comparable second-order finite volume schemes, with notable efficiency speedup due to parallelization.

Keywords: dam-break, discontinuous Galerkin scheme, flood modeling, shallow water equations

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Authors: Jian-Jun Shu

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It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Agoubi Belgacem, Adel Kharroubi

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Geothermal groundwater is the main water source to supply various sectors in El Hamma city, southeastern Tunisia. This region was long the destination of thousands of people from Tunisia and neighboring countries for care and bathing. The main objective of this study is to understand the groundwater mineralization origins and factors that control. The second goal is the appraisal of radon in geothermal groundwater in the study area. For this aim, geothermal groundwater was sampled and collected from different locations (thermal baths and deep wells). Physical parameters were measured and major ions were analyzed. Results reveal three water types. The water first type has Na-Mg-Ca-SO4-Cl facies and T>55°C. The second water type dominated by Na-Ca-Cl-SO4 facies with a temperature < 45 °C. However the third water type is dominated by Ca-SO4-Na-Cl-Mg. The three water types may be controlled by depth and geology. The first represent groundwater from deep aquifer (lower cretaceous), the second type was the shallow aquifer and the first is mixed water from deep and shallow water with a temperature ranging from 45 to 55°C. Measured Radon shows that shallow aquifer has a higher 222Rn concentration (677 to 2903 Bq.m-3) than deep water (203 to 1100 Bq.m-3). R-222 in El Hamma thermal aquifer was controlled by structures, porosity and permeability of aquifers. Geostatistical analyses of hydrogeological data and radon activities confirm the vertical flow and communication between deep and shallow aquifers through vertical faults system.

Keywords: Radon-222, geothermal, water, environment, Tunisia

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Authors: Almalki M., Alajmi M., Qadrouh Y., Alzahrani E., Sulaiman A., Aleid M., Albaiji A., Alfaifi H., Alhadadi A., Almotairy H., Alrasheed R., Alhafedh Y.

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High-resolution marine seismic survey is a well-established technique that commonly used to characterize near-surface sediments and geological structures at shallow water. We conduct single channel seismic survey to provide high quality seismic images for near-surface sediments upto 100m depth at Jubal costal area, Arabian Gulf. Eight hydrophones streamer has been used to collect stacked seismic traces alone 5km seismic line. To reach the required depth, we have used spark system that discharges energies above 5000 J with expected frequency output span the range from 200 to 2000 Hz. A suitable processing flow implemented to enhance the signal-to-noise ratio of the seismic profile. We have found that shallow sedimentary layers at the study site have complex pattern of reflectivity, which decay significantly due to amount of source energy used as well as the multiples associated to seafloor. In fact, the results reveal that single channel marine seismic at shallow water is a cost-effective technique that can be easily repeated to observe any possibly changes in the wave physical properties at the near surface layers

Keywords: shallow marine single-channel data, high resolution, frequency filtering, shallow water

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Authors: Rafat Alshorman, Fadi Awawdeh

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By employing a simplified bilinear method, a class of generalized fifth-order KdV (gfKdV) equations which arise in nonlinear lattice, plasma physics and ocean dynamics are investigated. With the aid of symbolic computation, both solitary wave solutions and multiple-soliton solutions are obtained. These new exact solutions will extend previous results and help us explain the properties of nonlinear solitary waves in many physical models in shallow water. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the coefficient parameters in the equation.

Keywords: multiple soliton solutions, fifth-order evolution equations, Cole-Hopf transformation, Hirota bilinear method

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Authors: Mustapha Kamel Mihoubi, Hocine Dahmani

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The purpose of work is to study the phenomenon of agitation of storm waves at basin caused by different directions of waves relative to the current provision thrown numerical model based on the equation in shallow water using Boussinesq model MIKE 21 BW. According to the diminishing effect of penetration of a wave optimal solution will be available to be reproduced in reduced model. Another alternative arrangement throws will be proposed to reduce the agitation and the effects of the swell reflection caused by the penetration of waves in the harbor.

Keywords: agitation, Boussinesq equations, combination, harbor

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Authors: S. Mehrab Amiri, Nasser Talebbeydokhti

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Modeling sediment transport processes by means of numerical approach often poses severe challenges. In this way, a number of techniques have been suggested to solve flow and sediment equations in decoupled, semi-coupled or fully coupled forms. Furthermore, in order to capture flow discontinuities, a number of techniques, like artificial viscosity and shock fitting, have been proposed for solving these equations which are mostly required careful calibration processes. In this research, a numerical scheme for solving shallow water and Exner equations in fully coupled form is presented. First-Order Centered scheme is applied for producing required numerical fluxes and the reconstruction process is carried out toward using Monotonic Upstream Scheme for Conservation Laws to achieve a high order scheme.  In order to satisfy C-property of the scheme in presence of bed topography, Surface Gradient Method is proposed. Combining the presented scheme with fourth order Runge-Kutta algorithm for time integration yields a competent numerical scheme. In addition, to handle non-prismatic channels problems, Cartesian Cut Cell Method is employed. A trained Multi-Layer Perceptron Artificial Neural Network which is of Feed Forward Back Propagation (FFBP) type estimates sediment flow discharge in the model rather than usual empirical formulas. Hydrodynamic part of the model is tested for showing its capability in simulation of flow discontinuities, transcritical flows, wetting/drying conditions and non-prismatic channel flows. In this end, dam-break flow onto a locally non-prismatic converging-diverging channel with initially dry bed conditions is modeled. The morphodynamic part of the model is verified simulating dam break on a dry movable bed and bed level variations in an alluvial junction. The results show that the model is capable in capturing the flow discontinuities, solving wetting/drying problems even in non-prismatic channels and presenting proper results for movable bed situations. It can also be deducted that applying Artificial Neural Network, instead of common empirical formulas for estimating sediment flow discharge, leads to more accurate results.

Keywords: artificial neural network, morphodynamic model, sediment continuity equation, shallow water equations

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Authors: Hitendra Raj Joshi, Bipin Lamichhane

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Groundwater is the main source of water for the industries of Balaju Industrial District (BID) and the denizens of Balaju-Boratar area. The quantity of groundwater is in a fatal condition in the area than earlier days. Water levels in shallow wells have highly lowered and deep wells are not providing an adequate amount of water as before because of higher extraction rate than the recharge rate. The main recharge zone of the shallow aquifer lies at the foot of Nagarjuna mountain, where recent colluvial debris are accumulated. Urbanization in the area is the main reason for decreasing water table. Recharge source for the deep aquifer in the region is aquiclude leakage. Sand layer above the Kalimati clay is the shallow aquifer zone, which is limited only in Balaju and eastern part of the Boratar, while the layer below the Kalimati clay spreading around Gongabu, Machhapohari, and Balaju area is considered as a potential area of deep aquifer. Over extraction of groundwater without considering water balance in the aquifers may dry out the source and can initiate the land subsidence problem. Hence, all the responsible of the industries in BID area and the denizens of Balaju-Boratar area should be encouraged to practice artificial groundwater recharge.

Keywords: aquiclude leakage, Kalimati clay, groundwater recharge

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Authors: Alia Alghosoun, Nabil El Moçayd, Mohammed Seaid

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Modeling dam-break flows over non-flat beds requires an accurate representation of the topography which is the main source of uncertainty in the model. Therefore, developing robust and accurate techniques for reconstructing topography in this class of problems would reduce the uncertainty in the flow system. In many hydraulic applications, experimental techniques have been widely used to measure the bed topography. In practice, experimental work in hydraulics may be very demanding in both time and cost. Meanwhile, computational hydraulics have served as an alternative for laboratory and field experiments. Unlike the forward problem, the inverse problem is used to identify the bed parameters from the given experimental data. In this case, the shallow water equations used for modeling the hydraulics need to be rearranged in a way that the model parameters can be evaluated from measured data. However, this approach is not always possible and it suffers from stability restrictions. In the present work, we propose an adaptive optimal control technique to numerically identify the underlying bed topography from a given set of free-surface observation data. In this approach, a minimization function is defined to iteratively determine the model parameters. The proposed technique can be interpreted as a fractional-stage scheme. In the first stage, the forward problem is solved to determine the measurable parameters from known data. In the second stage, the adaptive control Ensemble Kalman Filter is implemented to combine the optimality of observation data in order to obtain the accurate estimation of the topography. The main features of this method are on one hand, the ability to solve for different complex geometries with no need for any rearrangements in the original model to rewrite it in an explicit form. On the other hand, its achievement of strong stability for simulations of flows in different regimes containing shocks or discontinuities over any geometry. Numerical results are presented for a dam-break flow problem over non-flat bed using different solvers for the shallow water equations. The robustness of the proposed method is investigated using different numbers of loops, sensitivity parameters, initial samples and location of observations. The obtained results demonstrate high reliability and accuracy of the proposed techniques.

Keywords: erodible beds, finite element method, finite volume method, nonlinear elasticity, shallow water equations, stresses in soil

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Authors: Chunyue Liu, Hongxing Jiang

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Traditional water depth survey of wetland habitats used by waterbirds needs intensive labor, time and money. The optical remote sensing image relies on passive multispectral scanner data has been widely employed to study estimate water depth. This paper presents an innovative method for developing the water depth model based on the characteristics of visible and thermal infrared spectra of Landsat ETM+ image, combing with 441 field water depth data at Etoupao shallow wetland. The wetland is located at Momoge National Nature Reserve of Northeast China, where the largest stopover habitat along the eastern flyway of globally, critically-endangered Siberian Cranes are. The cranes mainly feed on the tubers of emergent aquatic plants such as Scirpus planiculmis and S. nipponicus. The effective water control is a critical step for maintaining the production of tubers and food availability for this crane. The model employing multi-band approach can effectively simulate water depth for this shallow wetland. The model parameters of NDVI and GREEN indicated the vegetation growth and coverage affecting the reflectance from water column change are uneven. Combining with the field-observed water level at the same date of image acquisition, the digital elevation model (DEM) for the underwater terrain was generated. The wetland area and water volume of different water levels were then calculated from the DEM using the function of Area and Volume Statistics under the 3D Analyst of ArcGIS 10.0. The findings provide good references to effectively monitor changes in water level and water demand, develop practical plan for water level regulation and water management, and to create best foraging habitats for the cranes. The methods here can be adopted for the bottom topography simulation and water management in waterbirds’ habitats, especially in the shallow wetlands.

Keywords: remote sensing, water depth reversion, shallow wetland habitat management, siberian crane

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Authors: A. Bahmanpour, I. Eames, C. Klettner, A. Dimakopoulos

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We develop a new set of diagnostic tools to analyze inundation into a model district using three-dimensional CFD simulations, with a view to generating a database against which to test simpler models. A three-dimensional model of Oregon city with different-sized groups of building next to the coastline is used to run calculations of the movement of a long period wave on the shore. The initial and boundary conditions of the off-shore water are set using a nonlinear inverse method based on Eulerian spatial information matching experimental Eulerian time series measurements of water height. The water movement is followed in time, and this enables the pressure distribution on every surface of each building to be followed in a temporal manner. The three-dimensional numerical data set is validated against published experimental work. In the first instance, we use the dataset as a basis to understand the success of reduced models - including 2D shallow water model and reduced 1D models - to predict water heights, flow velocity and forces. This is because models based on the shallow water equations are known to underestimate drag forces after the initial surge of water. The second component is to identify critical flow features, such as hydraulic jumps and choked states, which are flow regions where dissipation occurs and drag forces are large. Finally, we describe how future tsunami inundation models should be modified to account for the complex effects of buildings through drag and blocking.Financial support from UCL and HR Wallingford is greatly appreciated. The authors would like to thank Professor Daniel Cox and Dr. Hyoungsu Park for providing the data on the Seaside Oregon experiment.

Keywords: computational fluid dynamics, extreme events, loading, tsunami

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Authors: Mohammad R. Jalali

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Movement of liquid with a free surface in a container is known as slosh. For instance, slosh occurs when water in a closed tank is set in motion by a free surface displacement, or when liquid natural gas in a container is vibrated by an external driving force, such as an earthquake or movement induced by transport. Slosh is also derived from resonant switching of a natural basin. During sloshing, different types of motion are produced by energy exchange between the liquid and its container. In present study, a numerical model is developed to simulate the nonlinear even harmonic oscillations of free surface sloshing of an initial disturbance to the free surface of a liquid in a closed square basin. The response of the liquid free surface is affected by amplitude and motion frequencies of its container; therefore, sloshing involves complex fluid-structure interactions. In the present study, nonlinear interaction of free surface sloshing of an initial Gaussian hump with its uneven container is predicted numerically. For this purpose, Green-Naghdi (GN) equations are applied as governing equation of fluid field to produce nonlinear second-order and higher-order wave interactions. These equations reduce the dimensions from three to two, yielding equations that can be solved efficiently. The GN approach assumes a particular flow kinematic structure in the vertical direction for shallow and deep-water problems. The fluid velocity profile is finite sum of coefficients depending on space and time multiplied by a weighting function. It should be noted that in GN theory, the flow is rotational. In this study, GN numerical simulations of initial Gaussian hump are compared with Fourier series semi-analytical solutions of the linearized shallow water equations. The comparison reveals that satisfactory agreement exists between the numerical simulation and the analytical solution of the overall free surface sloshing patterns. The resonant free surface motions driven by an initial Gaussian disturbance are obtained by Fast Fourier Transform (FFT) of the free surface elevation time history components. Numerically predicted velocity vectors and magnitude contours for the free surface patterns indicate that interaction of Gaussian hump with its container has localized effect. The result of this sloshing is applicable to the design of stable liquefied oil containers in tankers and offshore platforms.

Keywords: fluid-structure interactions, free surface sloshing, Gaussian hump, Green-Naghdi equations, numerical predictions

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Authors: Serin Darwish, Hakim Saibi, Amir Gabr

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The United Arab Emirates (UAE) is situated within an arid zone where the climate is arid and the recharge of the groundwater is very low. Groundwater is the primary source of water in the United Arab Emirates. However, rapid expansion, population growth, agriculture, and industrial activities have negatively affected these limited water resources. The shortage of water resources has become a serious concern due to the over-pumping of groundwater to meet demand. In addition to the deficit of groundwater, the UAE has one of the highest per capita water consumption rates in the world. In this study, a combination of time-lapse measurements of microgravity and depth to groundwater level in selected wells in Al Ain city was used to estimate the variations in groundwater storage. Al-Ain is the second largest city in Abu Dhabi Emirates and the third largest city in the UAE. The groundwater in this region has been overexploited. Relative gravity measurements were acquired using the Scintrex CG-6 Autograv. This latest generation gravimeter from Scintrex Ltd provides fast, precise gravity measurements and automated corrections for temperature, tide, instrument tilt and rejection of data noise. The CG-6 gravimeter has a resolution of 0.1μGal. The purpose of this study is to measure the groundwater storage changes in the shallow aquifers based on the application of microgravity method. The gravity method is a nondestructive technique that allows collection of data at almost any location over the aquifer. Preliminary results indicate a possible relationship between microgravity and water levels, but more work needs to be done to confirm this. The results will help to develop the relationship between monthly microgravity changes with hydrological and hydrogeological changes of shallow phreatic. The study will be useful in water management considerations and additional future investigations.

Keywords: Al-Ain, arid region, groundwater, microgravity

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Authors: Hai Zhou, Wenzhi Zhao

Abstract:

Water is one of the most important factors limiting plant growth and development in desert ecosystems. In order to understand how desert shrubs cope with variation in water sources over time, it is important to understand plant–water relations in desert-oasis ecotone. We selected the typical desert shrubs: Nitraria sibirica, Calligonum mongolicum and Haloxylon ammodendron of 5-, 10-, 20- and 40-year old as the research species, to study the seasonal variation of plant water sources and response to precipitation in the desert-oasis ecotone of Linze, Northwestern China. We examined stable isotopic ratios of oxygen (δ18O) in stem water of desert shrubs as well as in precipitation, groundwater, and soil water in different soil layers and seasons to determine water sources for the shrubs. We found that the N. sibirica and H. ammodendron of 5-, 10-year old showed significant seasonal variation characteristics of δ18O value of stem water and water sources. However, the C. mongolicum and 20- and 40-year H. ammodendron main water sources were from deep soil water and groundwater, and less response to precipitation pulse. After 22.4 mm precipitation, the contribution of shallow soil water (0-50cm) to the use of N. sibirica increased from 6.7% to 36.5%; the C. mongolicum rarely use precipitation that were about 58.29% and 23.51%, absorbed from the deep soil water and groundwater; the contribution of precipitation to use of H. ammodendron had significantly differences among the four ages. The H. ammodendron of 5- and 10-year old about 86.3% and 42.5% water sources absorbed from the shallow soil water after precipitation. However, the contribution to 20- and 40-year old plant was less than 15%. So, the precipitation was one of the main water sources for desert shrubs, but the species showed different water utilization. We conclude that the main water source of the N. sibirica and H. ammodendron of 5-, 10-year was soil water recharged by precipitation, but the deeply rooted H. ammodendron of 20‐ and 40‐year‐old and the C. mongolicum have the ability to exploit a deep and reliable water source.

Keywords: water use pattern, water resource, stable isotope, seasonal change, precipitation pulse

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Authors: A. Shafaghat, H. Khabbaz, S. Moravej, Ah. Shafaghat

Abstract:

The bearing capacity of closely spaced shallow footings alters with their spacing and the shape of footing. In this study, the bearing capacity and settlement of two adjacent footings constructed on a sand layer are investigated. The effect of different footing shapes including square, circular, ring and strip on sandy soil is captured in the calculations. The investigations are carried out numerically using PLAXIS-3D software and analytically employing conventional settlement equations. For this purpose, foundations are modelled in the program with practical dimensions and various spacing ratios ranging from 1 to 5. The spacing ratio is defined as the centre-to-centre distance to the width of foundations (S/B). Overall, 24 models are analyzed; and the results are compared and discussed in detail. It can be concluded that the presence of adjacent foundation leads to the reduction in bearing capacity for round shape footings while it can increase the bearing capacity of rectangular footings in some specific distances.

Keywords: bearing capacity, finite element analysis, loose sand, settlement equations, shallow foundation

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Authors: Azubuike Ekwere

Abstract:

The shallow and deep aquiferous horizons of the fractured and weathered crystalline basement Oban Massif of south-eastern Nigeria were studied during the dry and wet seasons. The criteria were ascertaining hydrochemistry relative to seasonal and spatial variations across the study area. Results indicate that concentrations of major cations and anions exhibit the order of abundance; Ca>Na>Mg>K and HCO3>SO4>Cl respectively, with minor variations across sampling seasons. Major elements Ca, Mg, Na and K were higher for the shallow aquifers than the deep aquifers across seasons. The major anions Cl, SO4, HCO3, and NO3 were higher for the deep aquifers compared to the shallow ones. Two water types were identified for both aquifer types: Ca-Mg-HCO3 and Ca-Na-Cl-SO4. Most of the parameters considered were within the international limits for drinking, domestic and irrigation purposes. Assessment by use of sodium absorption ratio (SAR), percent sodium (%Na) and the wilcox diagram reveals that the waters are suitable for irrigation purposes.

Keywords: shallow aquifer, deep aquifer, seasonal variation, hydrochemistry, Oban massif, Nigeria

Procedia PDF Downloads 622

Authors: Mustafa Aytekin

Abstract:

In this study, impact of adjacent footings is considered on the estimation of elastic settlement of shallow foundations. In the estimation of elastic settlement, the Schmertmann’s method that is a very popular method in the elastic settlement estimation of shallow foundations is employed. In order to consider affect of neighboring footings on elastic settlement of main footing in different configurations, a MATLAB script has been generated. Elastic settlements of the various configurations are estimated by the script and several conclusions have been reached.

Keywords: elastic (immediate) settlement, Schmertman Method, adjacent footings, shallow foundations

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Authors: Barun Raychaudhuri

Abstract:

A methodology is proposed for estimating the optical attenuation and proportional depth variation of shallow inland water. The process is demonstrated with EO-1 Hyperion hyperspectral and IRS-P6 LISS-3 multispectral images of Kolkata city nearby area centered around 22º33′ N 88º26′ E. The attenuation coefficient of water was found to change with fine resolution of wavebands and in presence of suspended organic matter in water.

Keywords: hyperion, hyperspectral, Kolkata, water depth

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Authors: Arash Ghahraman, Gyula Bene

Abstract:

The object of this study is to investigate the effect of viscosity on the propagation of free-surface waves in an incompressible viscous fluid layer of arbitrary depth. While we provide a more detailed study of properties of linear surface waves, the description of fully nonlinear waves in terms of KdV-like (Korteweg-de Vries) equations is discussed. In the linear case, we find that in shallow enough fluids, no surface waves can propagate. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for any given horizontal wave number. The numerical results show that there can be two types of non-propagating modes. One type is always present, and there exist still infinitely many of such modes at the same parameters. In contrast, there can be zero, one or two modes belonging to the other type. Another significant feature is that KdV-like equations. They describe propagating nonlinear viscous surface waves. Since viscosity gives rise to a new wavenumber that cannot be small at the same time as the original one, these equations may not exist. Nonetheless, we propose a reasonable nonlinear description in terms of 1+1 variate functions that make possible successive approximations.

Keywords: free surface wave, water waves, KdV equation, viscosity

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Authors: I GD Yudha Partama, A. Kanno, Y. Akamatsu, R. Inui, M. Goto, M. Sekine

Abstract:

The aerial photogrammetry of shallow water bottoms has the potential to be an efficient high-resolution survey technique for shallow water topography, thanks to the advent of convenient UAV and automatic image processing techniques Structure-from-Motion (SfM) and Multi-View Stereo (MVS)). However, it suffers from the systematic overestimation of the bottom elevation, due to the light refraction at the air-water interface. In this study, we present an empirical method to correct for the effect of refraction after the usual SfM-MVS processing, using common software. The presented method utilizes the empirical relation between the measured true depth and the estimated apparent depth to generate an empirical correction factor. Furthermore, this correction factor was utilized to convert the apparent water depth into a refraction-corrected (real-scale) water depth. To examine its effectiveness, we applied the method to two river sites, and compared the RMS errors in the corrected bottom elevations with those obtained by three existing methods. The result shows that the presented method is more effective than the two existing methods: The method without applying correction factor and the method utilizes the refractive index of water (1.34) as correction factor. In comparison with the remaining existing method, which used the additive terms (offset) after calculating correction factor, the presented method performs well in Site 2 and worse in Site 1. However, we found this linear regression method to be unstable when the training data used for calibration are limited. It also suffers from a large negative bias in the correction factor when the apparent water depth estimated is affected by noise, according to our numerical experiment. Overall, the good accuracy of refraction correction method depends on various factors such as the locations, image acquisition, and GPS measurement conditions. The most effective method can be selected by using statistical selection (e.g. leave-one-out cross validation).

Keywords: bottom elevation, MVS, river, SfM

Procedia PDF Downloads 282