• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.53-65
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• 2003

Here we present a study of small-amplitude, shallow water waves on sloping beds. The beds considered in this analysis are linear and quadratic in nature. First we start with stating the relevant governing equations and boundary conditions for the theory of water waves. Once the complete prescription of the water-wave problem is available based on some assumptions (like inviscid, irrotational flow), we normalize it by introducing a suitable set of non-dimensional variables and then we scale the variables with respect to the amplitude parameter. This helps us to characterize the various types of approximation. In the process, a summary of equations that represent different approximations of the water-wave problem is stated. All the relevant equations are presented in rectangular Cartesian coordinates. Then we derive the equations and boundary conditions for small-amplitude and shallow water waves. Two specific types of bed are considered for our calculations. One is a bed with constant slope and the other bed has a quadratic form of surface. These are solved by using separation of variables method.

• Journal of Coastal Disaster Prevention
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• v.1 no.1
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• pp.1-9
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• 2014

In order to examine the characteristics of tsunami run-up heights on impermeable/permeable slope, a numerical wave tank by upgrading LES-WASS-3D was used in this study. Then, the model were compared with existing hydraulic model test for its verification. The numerical results well reproduced experimental results of solitary wave deformation, propagation and run-up height under various conditions. Also, the numerical simulation with a slope boundary condition has been carried out to understand solitary wave run-up on impermeable/permeable slope. It is shown that the run-up heights on permeable slope is 52.64-63.2% smaller than those on the impermeable slope because of wave energy dissipation inside the porous media. In addition, it is revealed that the numerical results with slope boundary condition agreed well with experimental results in comparison with the results by using stair type boundary condition.

• Journal of Ocean Engineering and Technology
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• v.17 no.6
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• pp.7-15
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• 2003

A Digital Wave Tank simulation technique, based on a finite-difference method and a modified marker-and-cell (MAC) algorithm, is applied in order to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach, Ohkushiri Island, and to predict maximum wove run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain, and the boundary values are updated at each time step, by a finite-difference time-marching scheme in the frame of the rectangular coordinate system. The fully nonlinear, kinematic, free-surface condition is satisfied by the modified marker-density function technique. The near shore Tsunami is assumed to be a solitary wave, and is generated from the numerical wave-maker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods, based on the shallow-water wave theory.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2003.05a
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• pp.231-239
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• 2003

A Digital Wave Tank simulation technique based on a finite-difference method and a modified marker-and-cell (MAC) algorithm is applied to investigate the characteristics of nonlinear Tsunami propagations and their interactions with a 2D sloping beach and Ohkushiri island, and to predict maximum wave run-up around the island. The Navier-Stokes (NS) and continuity equation are governed in the computational domain and the boundary values updated at each time step by a finite-difference time-marching scheme in the frame of rectangular coordinate system. The fully nonlinear kinematic free-surface condition is satisfied by the modified marker-density function technique. The Nearshore Tsunami is assumed to be a solitary wave and generated from the numerical wavemaker in the developed Digital Wave Tank. The simulation results are compared with the experiments and other numerical methods based on the shallow-water wave theory.

• Water for future
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• v.29 no.3
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• pp.163-176
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• 1996

When a pipe is deployed on a sloping bed, pumping power required for a discharge can be estimated immediately without any iteration process with an explicit form of a friction factor equation. Pumping power being given, however, traditional method requires an iteration process for the solution of discharge and pipe diameter even for the uniformly-rough pipe. You (1955b) has suggested explicit equations for the estimation of discharge and pipe diameter particularly for the cases of pipe on a slopintg bed without pumping and pipe on a horizontal bed with a pumping power. Based on his approach and previous results, the present researchers have developed explicit equations of discharge and pipe diameter for the general case of pipe on a sloping bed with a pumping power. The equations of boundary criteria are also presented in explicit way which render proper choice of various equations suitable for the flow condition between five characteristics. Verification studies are also carried out by applying the explicit equations to a practical example.