• Title/Summary/Keyword: depth averaged equation

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Numerical Simulation of Solitary Wave Run-up with an Internal Wave-Maker of Navier-Stokes Equations Model (내부조파기법을 활용한 Navier-Stokes 방정식 모형의 고립파 처오름 수치모의)

  • Ha, Tae-Min;Kim, Hyung-Jun;Cho, Yong-Sik
    • Journal of Korea Water Resources Association
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    • v.43 no.9
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    • pp.801-811
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    • 2010
  • A three-dimensional numerical model called NEWTANK is employed to investigate solitary wave run-up with an internal wave-maker on a steep slope. The numerical model solves the spatially averaged Navier-Stokes equations for two-phase flows. The LES (large-eddy-simulation) approach is adopted to model the turbulence effect by using the Smagorinsky SGS (sub-grid scale) closure model. A two-step projection method is adopted in numerical solutions, aided by the Bi-CGSTAB (Bi-Conjugate Gradient Stabilized) method to solve the pressure Poisson equation for the filtered pressure field. The second-order accurate VOF (volume-of-fluid) method is used to track the distorted and broken free surface. A solitary wave is first internally generated and propagated over a constant water depth in the three-dimensional domain. Numerically predicted results are compared with analytical solutions and numerical errors are analyzed in detail. The model is then applied to study solitary wave run-up on a steep slope and the obtained results are compared with available laboratory measurements.

STUDIES ON THE PROPAGATION OF ABALONE (전복의 증식에 관한 연구)

  • PYEN Choong-Kyu
    • Korean Journal of Fisheries and Aquatic Sciences
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    • v.3 no.3
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    • pp.177-186
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    • 1970
  • The spawning of the abalone, Haliotis discus hannai, was induced In October 1969 by air ex-position for about 30 minutes. At temperatures of from 14.0 to $18.8^{\circ}C$, the youngest trochophore stage was reached within 22 hours after the egg was laid. The trochophore was transformed into the veliger stage within 34 hours after fertilization. For $7\~9$ days after oviposition the veliger floated in sea water and then settled to the bottom. The peristomal shell was secreted along the outer lip of the aperture of the larval shell, and the first respiratory pore appears at about 110 days after fertilization. The shell attained a length of 0.40 mm in 15 days, 1.39 mm in 49 days, 2.14 mm in 110 days, 5.20 mm in 170 days and 10.00 mm in 228 days respectively. Monthly growth rate of the shell length is expressed by the following equation :$L=0.9981\;e^{0.18659M}$ where L is shell length and M is time in month. The density of floating larvae in the culture tank was about 10 larvae per 100 co. The number of larvae attached to a polyethylene collector ($30\times20\;cm$) ranged from 10 to 600. Mortality of the settled larvae on the polyethylene collector was about $87.0\%$ during 170 days following settlement. The culture of Nauicula sp. was made with rough polyethylene collectors hung at three different depths, namely 5 cm, 45 cm and 85 cm. At each depth the highest cell concentration appeared after $15\~17$ days, and the numbers of cells are shown as follows: $$5\;cm\;34.3\times10^4\;Cells/cm^2$$ $$45\;cm\;27.2\times10^4\;Cells/cm^2$$ $$85\;cm\;26.3\times10^4\;Cells/cm^2$$ At temperatures of from 13.0 to $14.3^{\circ}C$, the distance travelled by the larvae (3.0 mm In shell length) averaged 11.36 mm for a Period of 30 days. Their locomation was relatively active between 6 p.m. and 9 p.m., and $52.2\%$ of them moved during this period. When the larvae (2.0 mm in shell length) were kept in water at $0\;to\;\~1.8^{\circ}C$, they moved 1.15cm between 4 p.m. and 8 p.m. and 0.10 cm between midnight and 8 a.m. The relationships between shell length and body weight of the abalone sampled from three different localities are shown as follows: Dolsan-do $W=0.2479\;L^{2.5721}$ Huksan-do $W=0.1001\;L^{3.1021}$ Pohang $W=0.9632\;L^{2.0611}$

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