Numerical Simulation of Tidal Currents in Persian Gulf

In this paper, a two-dimensional (2D) numerical model for the tidal currents simulation in Persian Gulf is presented. The model is based on the depth averaged equations of shallow water which consider hydrostatic pressure distribution. The continuity equation and two momentum equations including the effects of bed friction, the Coriolis effects and wind stress have been solved. To integrate the 2D equations, the Alternative Direction Implicit (ADI) technique has been used. The base of equations discritization was finite volume method applied on rectangular mesh. To evaluate the model validation, a dam break case study including analytical solution is selected and the comparison is done. After that, the capability of the model in simulation of tidal current in a real field is represented by modeling the current behavior in Persian Gulf. The tidal fluctuations in Hormuz Strait have caused the tidal currents in the area of study. Therefore, the water surface oscillations data at Hengam Island on Hormoz Strait are used as the model input data. The check point of the model is measured water surface elevations at Assaluye port. The comparison between the results and the acceptable agreement of them showed the model ability for modeling marine hydrodynamic.

Effect of Shallow Groundwater Table on the Moisture Depletion Pattern in Crop Root Zone

Different techniques for estimating seasonal water use from soil profile water depletion frequently do not account for flux below the root zone. Shallow water table contribution to supply crop water use may be important in arid and semi-arid regions. Development of predictive root uptake models, under influence of shallow water table makes it possible for planners to incorporate interaction between water table and root zone into design of irrigation projects. A model for obtaining soil moisture depletion from root zone and water movement below it is discussed with the objective to determine impact of shallow water table on seasonal moisture depletion patterns under water table depth variation, up to the bottom of root zone. The role of different boundary conditions has also been considered. Three crops: Wheat (Triticum aestivum), Corn (Zea mays) and Potato (Solanum tuberosum), common in arid & semi-arid regions, are chosen for the study. Using experimentally obtained soil moisture depletion values for potential soil moisture conditions, moisture depletion patterns using a non linear root uptake model have been obtained for different water table depths. Comparative analysis of the moisture depletion patterns under these conditions show a wide difference in percent depletion from different layers of root zone particularly top and bottom layers with middle layers showing insignificant variation in moisture depletion values. Moisture depletion in top layer, when the water table rises to root zone increases by 19.7%, 22.9% & 28.2%, whereas decrease in bottom layer is 68.8%, 61.6% & 64.9% in case of wheat, corn & potato respectively. The paper also discusses the causes and consequences of increase in moisture depletion from top layers and exceptionally high reduction in bottom layer, and the possible remedies for the same. The numerical model developed for the study can be used to help formulating irrigation strategies for areas where shallow groundwater of questionable quality is an option for crop production.

Tsunami Modelling using the Well-Balanced Scheme

A well balanced numerical scheme based on stationary waves for shallow water flows with arbitrary topography has been introduced by Thanh et al. [18]. The scheme was constructed so that it maintains equilibrium states and tests indicate that it is stable and fast. Applying the well-balanced scheme for the one-dimensional shallow water equations, we study the early shock waves propagation towards the Phuket coast in Southern Thailand during a hypothetical tsunami. The initial tsunami wave is generated in the deep ocean with the strength that of Indonesian tsunami of 2004.

A Shallow Water Model for Computing Inland Inundation Due to Indonesian Tsunami 2004 Using a Moving Coastal Boundary

In this paper, a two-dimensional mathematical model is developed for estimating the extent of inland inundation due to Indonesian tsunami of 2004 along the coastal belts of Peninsular Malaysia and Thailand. The model consists of the shallow water equations together with open and coastal boundary conditions. In order to route the water wave towards the land, the coastal boundary is treated as a time dependent moving boundary. For computation of tsunami inundation, the initial tsunami wave is generated in the deep ocean with the strength of the Indonesian tsunami of 2004. Several numerical experiments are carried out by changing the slope of the beach to examine the extent of inundation with slope. The simulated inundation is found to decrease with the increase of the slope of the orography. Correlation between inundation / recession and run-up are found to be directly proportional to each other.

Splitting Modified Donor-Cell Schemes for Spectral Action Balance Equation

The spectral action balance equation is an equation that used to simulate short-crested wind-generated waves in shallow water areas such as coastal regions and inland waters. This equation consists of two spatial dimensions, wave direction, and wave frequency which can be solved by finite difference method. When this equation with dominating propagation velocity terms are discretized using central differences, stability problems occur when the grid spacing is chosen too coarse. In this paper, we introduce the splitting modified donorcell scheme for avoiding stability problems and prove that it is consistent to the modified donor-cell scheme with same accuracy. The splitting modified donor-cell scheme was adopted to split the wave spectral action balance equation into four one-dimensional problems, which for each small problem obtains the independently tridiagonal linear systems. For each smaller system can be solved by direct or iterative methods at the same time which is very fast when performed by a multi-cores computer.

Discontinuous Galerkin Method for 1D Shallow Water Flow with Water Surface Slope Limiter

A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing Runge- Kutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-dimensional shallow water equations. For each slope limiter, three different Riemann solvers based on HLL, LF, and Roe flux functions are used. The proposed water surface based slope limiter scheme is easy to implement and shows better conservation property compared to the slope limiter based on water depth. Of the three flux functions, the Roe approximation provides the best results while the LF function proves to be least suitable when used with either slope limiter scheme.

Simulation of Sloshing-Shear Mixed Shallow Water Waves (II) Numerical Solutions

This is the second part of the paper. It, aside from the core subroutine test reported previously, focuses on the simulation of turbulence governed by the full STF Navier-Stokes equations on a large scale. Law of the wall is found plausible in this study as a model of the boundary layer dynamics. Model validations proceed to include velocity profiles of a stationary turbulent Couette flow, pure sloshing flow simulations, and the identification of water-surface inclination due to fluid accelerations. Errors resulting from the irrotational and hydrostatic assumptions are explored when studying a wind-driven water circulation with no shakings. Illustrative examples show that this numerical strategy works for the simulation of sloshing-shear mixed flow in a 3-D rigid rectangular base tank.

Time Domain and Frequency Domain Analyses of Measured Metocean Data for Malaysian Waters

Data of wave height and wind speed were collected from three existing oil fields in South China Sea – offshore Peninsular Malaysia, Sarawak and Sabah regions. Extreme values and other significant data were employed for analysis. The data were recorded from 1999 until 2008. The results show that offshore structures are susceptible to unacceptable motions initiated by wind and waves with worst structural impacts caused by extreme wave heights. To protect offshore structures from damage, there is a need to quantify descriptive statistics and determine spectra envelope of wind speed and wave height, and to ascertain the frequency content of each spectrum for offshore structures in the South China Sea shallow waters using measured time series. The results indicate that the process is nonstationary; it is converted to stationary process by first differencing the time series. For descriptive statistical analysis, both wind speed and wave height have significant influence on the offshore structure during the northeast monsoon with high mean wind speed of 13.5195 knots ( = 6.3566 knots) and the high mean wave height of 2.3597 m ( = 0.8690 m). Through observation of the spectra, there is no clear dominant peak and the peaks fluctuate randomly. Each wind speed spectrum and wave height spectrum has its individual identifiable pattern. The wind speed spectrum tends to grow gradually at the lower frequency range and increasing till it doubles at the higher frequency range with the mean peak frequency range of 0.4104 Hz to 0.4721 Hz, while the wave height tends to grow drastically at the low frequency range, which then fluctuates and decreases slightly at the high frequency range with the mean peak frequency range of 0.2911 Hz to 0.3425 Hz.

Simulation of Dam Break using Finite Volume Method

Today, numerical simulation is a powerful tool to solve various hydraulic engineering problems. The aim of this research is numerical solutions of shallow water equations using finite volume method for Simulations of dam break over wet and dry bed. In order to solve Riemann problem, Roe-s approximate solver is used. To evaluate numerical model, simulation was done in 1D and 2D states. In 1D state, two dam break test over dry bed (with and without friction) were studied. The results showed that Structural failure around the dam and damage to the downstream constructions in bed without friction is more than friction bed. In 2D state, two tests for wet and dry beds were done. Generally in wet bed case, waves are propagated to canal sides but in dry bed it is not significant. Therefore, damage to the storage facilities and agricultural lands in wet bed case is more than in dry bed.

Linear Stability Characteristics of Wake-Shear Layers in Two-Phase Shallow Flows

Linear stability of wake-shear layers in two-phase shallow flows is analyzed in the present paper. Stability analysis is based on two-dimensional shallow water equations. It is assumed that the fluid contains uniformly distributed solid particles. No dynamic interaction between the carrier fluid and particles is expected in the initial moment. Linear stability curves are obtained for different values of the particle loading parameter, the velocity ratio and the velocity deficit. It is shown that the increase in the velocity ratio destabilizes the flow. The particle loading parameter has a stabilizing effect on the flow. The role of the velocity deficit is also destabilizing: the increase of the velocity deficit leads to less stable flow.