• Proceedings of the Korea Water Resources Association Conference
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• 2005.09b
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• pp.842-845
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• 2005

A method for the numerical simulation of two-dimensional free-surface flow resulting from the propagation of regular gravity waves over topography with arbitrary bottom shape is presented. The method is based on the numerical solution of the Euler equations subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions using a hybrid finite-differences and spectral-method scheme. The formulation includes a boundary-fitted transformation, and is suitable for extension to incorporate large-eddy simulation (LES) and large-wave simulation (LWS) terms for turbulence and breaking wave modeling, respectively. Results are presented for the simulation of the free-surface flow over two different bottom topographies, with constant slope values of 1:10 and 1:20, two different inflow wave lengths and two different inflow wave heights. An absorption outflow zone is utilized and the results indicate minimum wave reflection from the outflow boundary. Over the bottom slope, lengths of waves in the linear regime are modified according to linear theory dispersion, while wave heights remain more or less unchanged. For waves in the nonlinear regime, wave lengths are becoming shorter, while the free surface elevation deviates from its initial sinusoidal shape.

• Journal of the korean society of oceanography
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• v.32 no.3
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• pp.93-102
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• 1997

Coastal circulations during the (surface condition of an) idealized cold-air outbreak are numerically investigated with two-dimensional, non-hydrostatic model in which a constant bottom-slope exists. The atmospheric forcing during a cold-air outbreak is incorporated as the surface cooling and the wind stress. When the offshore angle of the wind-stress vector, defined as the angle measured from the alongshore axis, is smaller than 45 degrees, a strong downwelling circulation develops near the coast. A sharp density front, which separates the vertically homogeneous region from the offshore stratified region, is formed near the coast and propagates offshore with time. Onshore side of the density front, small-scale circulation cells which are aligned in the direction perpendicular to the bottom begin to develop as the near-coast homogeneous region broadens. The surface cooling enhances greatly the development of the surface mixed layer by convective motions due to hydrostatic instability. The convective motions reach far below the hydrostatically unstable layer which is attached to the surface. The small-scale circulation cells are appreciably modified by the convetion cell and the density front develops far offshore compared to the case of no surface cooling. As to the effect of the bottom slope, the offshore distance of the density front increases (decreases) as the bottom slope decreases (increases), which results from the fact that the onshore volume-transport (Ekman transport) of the low-density upper seawater remains almost constant when the wind-stress is maintained constant. It is shown that the bottom slope is an essential factor for the formation of both the density front and the alongshore current when the surface cooling is the only forcing.

• The Journal of the Acoustical Society of Korea
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• v.21 no.5
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• pp.485-493
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• 2002

Broadband interference patterns are studied using ship as an acoustic source in shallow waters with varying bathymetry. Waveguide invariant index (β) indicating the pattern of constructive (or destructive) interference in range-frequency domain is derived in a waveguide with constant bottom slope based on adiabatic mode theory. Using this invariant, changes of the interference patterns resulting from the variation of bottom bathymetry are analyzed. Results of the analytic interpretation is compared with those from sea experiments and numerical simulations.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.56 no.4
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• pp.395-406
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• 2020

The objectives of this study were to develop the optimal structures of recirculating aquaculture tank for improving the removal efficiency of solid materials and maintaining water quality conditions. Flow analysis was performed using the CFD (computational fluid dynamics) method to understand the hydrodynamic characteristics of the circular tank according to the angle of inclination in the tank bottom (0°, 1.5° and 3°), circulating water inflow method (underwater, horizontal nozzle, vertical nozzle and combination nozzle) and the number of inlets. As the angle in tank bottom increased, the vortex inside the tank decreased, resulting in a constant flow. In the case of the vertical nozzle type, the eddy flow in the tank was greatly improved. The vertical nozzle type showed excellent flow such as constant flow velocity distribution and uniform streamline. The combination nozzle type also showed an internal spiral flow, but the vortex reduction effect was less than the vertical nozzle type. As the number of inlets in the tank increased, problems such as speed reduction were compensated, resulting in uniform fluid flow.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.208-218
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• 1992

Analytic solutions for the gradient of surface elevation and vertical profiles of velocity driven by the wind stress in the one-dimensional rectangular basin were obtained under the assumption of steady-state. The approach treats the bottom frictional stress $\tau$$_{b}$ as known and includes vertically varying eddy viscosity $textsc{k}$$_{M}$, which is constant, linear and quadratic of water depth. When the $\tau$$_{b}$ is param-terized with surface stress, depth averaged velocity and bottom velocity, the result shows the relation of the no-slip bottom velocity condition and the bottom frictional stress $\tau$$_{b}$. The results of a mode splitted, (x-$\sigma$) coordinate, numerical model were compared with the derived analytic solutions. The comparison was made for the case such that $textsc{k}$$_{M}$ is the constant, linear and quadratic function of water depth. In the case of constant $textsc{k}$$_{M}$, the gradient of surface elevation and vertical profiles of velocity are discussed for a uniform depth, a mild slope and a relatively steep slope. When $textsc{k}$$_{M}$ is a linear and quadratic function of water depth, the vertical structures of velocities are discussed for various $\tau$$_{b}$. The result of the comparison shows that the vertical structure of velocities depends not only on the value of $textsc{k}$$_{M}$ but also on the profile of $textsc{k}$$_{M}$ and bottom stress $\tau$$_{b}$. Model results were in a good agreement with the analytic solutions considered in this study.his study.y.his study.

• Journal of Korean Port Research
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• v.7 no.1
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• pp.79-88
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• 1993

This study deals with the case of a fixed floating structure(FFS) at the mouth of a rectangular harbor under the action of waves represented by the linear wave theory. Modified forms of the mild-slope equation is applied to the propagation of regular wave over constant water depth. The model is extended to include bottom friction and boundary absorption. A hybrid element approximation is used for calculation of linear wave oscillation in and near coastal harbor. Modification of the model was necessary for the FFS. For the conditions tested, the results of laboratory experiments by Ippen and Goda(1963), and Lee (1969) are compared with the calculated one from this model. The cases of flat cylinderical structures, both fixed and floating, were taken to be in an intermediate water depth.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.19 no.5
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• pp.436-445
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• 2007

An analytical solution which can be applied to an arbitrarily varying topography is derived by using the continuity and momentum equations. Applying the fact that the solution of the governing equation is expressed as Bessel function in such case that the water depth varies linearly, the present solution is obtained by assuming the water depth as series of constant slope. The present solution is verified by comparing with analytical solution derived previously and investigates the effects of bottom topography to run-up height of vertical structure.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.22 no.2
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• pp.73-78
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• 2010

Wave energy is dissipated mainly by friction on the seabed until the waves reach the surf zone. Many researchers have investigated the mechanism of wave friction and the bottom shear stress induced by wave motion at a certain point is now well estimated by introducing the wave friction factor related to the near bed velocity given by linear wave theory. The variation of wave energy or wave height over a long distance can be, however, estimated by an iteration process when the propagation of waves is strongly influenced by bed friction. In the present study simple semi-theoretical equation has been developed to compute the variation of wave height for the condition of wave propagation on a constant beach slope. The ratio of wave height is determined by the product of shoalng factor and wave height friction factor (frictional wave energy dissipation factor). The wave height estimated by the new equation is compared with the wave height estimated by the solution of numerical integration for the condition that the waves propagate on a constant slope.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.5B
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• pp.467-474
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• 2011

Debris flow is one of the most hazardous natural processes in mountainous regions. The degradation of discharge capacity of drainage facilities due to debris flows may result in damages of properties and casualty as well as road. Understanding and accurate reproducing flow behaviour of debris flows at various conditions, such as sediment volume concentration and approaching channel and culvert slopes, are prerequisite to develop advanced design criteria for drainage facilities to prevent such damages. We carried out a series of laboratory experiments of debris flows in a rectangular channel of constant width with an abrupt change of bottom slope. The experimental flume consists of an approaching channel part with the bed slope ranging $15^{\circ}$ to $30^{\circ}$ and the test channel with slope ranging from $0^{\circ}$ to $12^{\circ}$ which mimics a typical drainage culvert. The experiments have been conducted for 22 test cases with various flow conditions of channel slopes and sediment volume concentration of debris flows to investigate those effects on the behaviour of debris flows. The results show that, according to sediment volume concentration, the depth of debris flow is approximately 50% to 150% larger than that of fresh water flow at the same flow rate. Experimental results quantitatively present that flow behaviour and deposit history of debris flows in the culvert depend on the slopes of the approaching and drainage channels and sediment volume concentration. Based on the experimental results, furthermore, a logistic model is developed to find the optimized culvert slope which prevents the debris flow from depositing in the culvert.

• 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.