• Bulletin of the Korean Mathematical Society
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• v.57 no.4
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• pp.891-907
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• 2020

In this paper, we consider the Cauchy problem to the tropical climate model. We establish the global regularity for the 2D tropical climate model with generalized nonlocal dissipation of the barotropic mode and obtain a multi-logarithmical vorticity blow-up criterion for the 2D tropical climate model without any dissipation of the barotropic mode.

• Journal of the Korean earth science society
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• v.38 no.3
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• pp.173-181
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• 2017

The stability of the steady Rossby-Haurwitz wave (R-H wave) in the nondivergent barotropic model (NBM) on the sphere was investigated with the normal mode method. The linearized NBM equation with respect to the R-H wave was formulated into the eigenvalue-eigenvector problem consisting of the huge sparse matrix by expanding the variables with the spherical harmonic functions. It was shown that the definite threshold R-H wave amplitude for instability could be obtained by the normal mode method. It was revealed that some unstable modes were stationary, which tend to amplify without the time change of the spatial structure. The maximum growth rate of the most unstable mode turned out to be in almost linear proportion to the R-H wave amplitude. As a whole, the growth rate of the unstable mode was found to increase with the zonal- and total-wavenumber. The most unstable mode turned out to consist of more-than-one zonal wavenumber, and in some cases, the mode exhibited a discontinuity over the local domain of weak or vanishing flow. The normal mode method developed here could be readily extended to the basic state comprised of multiple zonalwavenumber components as far as the same total wavenumber is given.

• Journal of Ocean Engineering and Technology
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• v.31 no.1
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• pp.1-7
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• 2017

There are two wave modes induced by an oscillating body on the free surface of a two-layer fluid: the barotropic and baroclinic modes. To investigate the generated waves composed of two modes, a radiation problem involving a heaving rectangular body was solved in a numerical wave tank. A new artificial damping zone scheme was developed and applied in the frequency-domain analysis. The performance of this damping scheme was compared with given radiation boundary conditions for various conditions. The added mass and radiation damping coefficients for the heaving rectangular body were also calculated for various fluid-density ratios.

• Ocean and Polar Research
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• v.23 no.2
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• pp.195-203
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• 2001

A fine-grid (3 km ${\times}$ 3 km), three-dimensional nowcast system of sea levels, currents, temperature, and salinity is being developed for the Taiwan Strait. The project takes a balanced approach relying equally on models and observations, will have the capacity of real-time data assimilation, and is aimed at both practical and scientific applications. To determine boundary conditions and verify model results, eight coastal tide-gauge stations were first established along both sides of the strait. Strait-wide hydrographic surveys were conducted by research vessels. Currents are being measured using bottom-mounted ADCP moorings in a meridional deep channel off southwest Taiwan and along a traverse section in the central part of the strait. In addition to a fine-resolution three-dimensional model of the Taiwan Strait, an adjoint model and a larger-domain two-dimensional model were used to better determine boundary conditions in the northern and southern boundaries of the strait. In the first stage of model development, barotropic tides were successfully simulated in a hindcast mode. The protocol product has been released to general public, including government agencies, universities and general users.

• 한국해양학회지
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• v.26 no.2
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• pp.133-143
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• 1991

A new internal tide model for solving flow fields and wave generations is presented here which seems to be simple to apply, converges fast and yields accurate results. The new method employs a representation of vertical structure using dynamic basis functions which depend on the stratifications. The present method has been applied to the East Sea. For a constant Brunt-Vaisala case, weak baroclinic currents are generated over the entire continertal slop: however, results using a more realistic stratification can be described using only the lowest modes and exhibit much more realistic behavior. Baroclinic tide generation is confined to the upper slope. Model results for the East sea show the semi-diurnal baroclinic modes contain almost all the energy transferred from the barotropic mode.

• Journal of the Korean earth science society
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• v.37 no.2
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• pp.107-116
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• 2016

Stability of the barotropic Rossby-Haurwitz wave is investigated using the numerical models on the global domain. The Rossby-Haurwitz wave under investigation is composed of the basic zonal flow of super-rotation and a finite amplitude spherical harmonic wave. The Rossby-Haurwitz wave is given as either steady or unsteady wave by adjusting the strength of the super-rotating zonal flow. Stability as well as the growth rate of the wave in the numerical simulation is determined by comparing the perturbation amplitude at two different time stages. Unstable modes of the Rossby-Haurwitz wave exhibited a horizontal structure composing of various zonal-wavenumber components. The vorticity perturbation for some modes showed a discontinuity around the area of weak flow, which was found robust regardless of the horizontal resolution of the model. Fourier finite element model was shown to generate the unstable mode in earlier stage of the time integration due to less accuracy compared to the spherical harmonic spectral model. Taking the overall accuracy of the models into consideration, the time by which the unstable mode begin to dominate over the spherical harmonic wave was estimated.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.12 no.2
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• pp.70-80
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• 2000

Princeton Ocean Model (POM) is modified to construct a three-dimensional, semi-implicit hydro¬dynamic model with a wetting-and-drying scheme. The model employs semi-implicit treatment of the barotropic pressure gradient terms and the vertical mixing terms in the momentum equations, and the velocity divergence term in the vertically-integrated continuity equation. Such treatment removes the external mode and thus the mode splitting scheme in POM, allowing the semi-implicit model to use a larger time step. Applied to hypothetical systems, both the semi-implicit model and POM give nearly the same results. The semi-implicit model, however, runs approximately 4.4 times faster than POM showing its improved computational efficiency. Applied to a hypothetical system with intertidal flats, POM employing the mode splitting scheme produces noises at the intertidal flats, that propagate into the main channel resulting in unstable current velocities. Despite its larger time step, the semi-implicit model gives stable current velocities both at the intertidal flats and main channel. The semi-implicit model when applied to Kyeonggi Bay gives a good reproduction of the observed tides and tidal currents throughout the modeling domain, demonstrating its prototype applicability.