• Journal of the Korean earth science society
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• v.41 no.4
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• pp.344-355
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• 2020

Tropical cyclone scale vortices and associated Rossby waves were investigated numerically using high-resolution barotropic models on the global domain. The equations of the barotropic model were discretized using the spectral transform method with the spherical harmonics function as orthogonal basis. The initial condition of the vortex was specified as an axisymmetric flow in the gradient wind balance, and four types of basic zonal states were employed. Vortex tracks showed similar patterns as those on the beta-plane but exhibited more eastward displacement as they moved northward. The zonal-mean flow appeared to control not only the west-east translation but also the meridional translation of the vortex. Such a meridional influence was revealed to be associated with the beta gyre and the Rossby wave, which are formed around the vortex due to the beta effect. In the case of the basic zonal state of climatological mean, the meridional translation speed reached the maximum value when the vortex underwent recurving.

• Journal of the Korean earth science society
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• v.35 no.5
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• pp.333-341
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• 2014

A new set of basis functions was constructed using the Rossby-Haurwitz waves, which are the eigenfunctions of nondivergent barotropic vorticity equations on the sphere. The basis functions were designed to be non-separable, that is, not factored into functions of either the longitude or the latitude. Due to this property, the nodal lines of the functions are aligned neither along with the meridian nor the parallel. The basis functions can be categorized into groups of which members have the same degree or the total wavenumber-like index on the sphere. The orthonormality of the basis functions were found to be close to the machine roundoffs, giving the error of $O(10^{-15})$ or $O(10^{-16})$ for double-precision computation (64 bit arithmetic). It was demonstrated through time-stepping procedure that the basis functions were also the eigenfunctions of the non-divergent barotropic vorticity equations. The projection of the basis functions was carried out onto the low-resolution geopotential field of Gaussian bell, and compared with the theory. The same projections were performed for the observed atmospheric-geopotential height field of 500 hPa surface to demonstrate decomposition into the fields that contain disturbance of certain range of horizontal scales. The usefulness of the new basis functions was thus addressed for application to the eigenmode analysis of the atmospheric motions on the global domain.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.24 no.6
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• pp.428-436
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• 1991

Double shelf topography allows the existence of two sets of waves propagating in opposite directons. In the case that two shelves are apart sufficiently enough, the solutions show two independent sets of waves which recover the single shelf waves. However, if the distance between two shelves is less than the Rossby deformation radius, the waves become dependent on the geometry of both shelves. Even over a double shelf topography, shelf waves propagate with the shallow water to the right in the Northern Hemisphere. The group velocity of shelf wave has the same direction as phase velocity in the long wave case, but the opposite direction in the short wave case. Each shelf mode has a zero group velocity at some intermediate value of wave length.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.25 no.6
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• pp.443-456
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• 1992

For a linear double shelf bottom topography as in the Yellow Sea, the dispersion relation of coastally trapped waves is derived for the general case Including high-frequency and short waves and for the case of low-frequency and long waves. With linear bottom topography, the governing equation is Bessel's equation for the latter case but Hummer's equation for the former case. Hypergeometric Functions, which are the solutions of Hummer's equation, are derived and converted to various special functions for the limiting cases. On a double shelf topography, the divergence effects of horizontal flow are important for the wave dynamics, irrespective of cross-shelf dimensions, while on a single shelf they are usually neglected when the cross-shelf dimension is much smaller than the Rossby deformation radius. The divergence effect allows the existence of Kelvin wave and reduces the phase speeds of continental shelf waves. Finally, the frictionless eigenfunctions are proved to be orthogonal.

• 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.

• Fisheries and Aquatic Sciences
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• v.1 no.1
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• pp.7-18
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• 1998

In order to understand the generation of the Sogcho Eddy due to the strong offshore winds, we first investigated the characteristics of winds at Sogcho, Kangnung and Samchuk, and then carried out a series of numerical experiments using the nonlinear 1 1/2-layer model. The models were forced by wind stress fields, similar in structure to the prevailing winds that a field in the east coast of Korea during the winter season. The winds were composed of the background winds $(-1\;dyne/cm^2)$ for 90 days and the local winds $(-4\;dyne/cm^2)$ for 30 days. The analysis of wind data at three stations (Sogcho, Kangnung, and Samchuk) showed that the wind was stronger in winter than in other seasons and the offshore component was much dominant. According to our numerical solutions, the Sogcho Eddy of about 200 km in diameter was generated due to the strong offshore winds prevailing in the Kangnung - Sogcho regions. The eastward propagation of the Rossby waves reflected at the western boundary resulted in the eastward meandering motion from the eastern side of the eddy.

• Journal of the Korean earth science society
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• v.36 no.5
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• pp.476-483
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• 2015

The high-order Laplacian-type filter, which is capable of providing isotropic and sharp cut-off filtering on the spherical domain, is essential in processing geophysical data. In this study, a spherical high-order filter was designed by combining the Fourier method with finite difference-method in the longitude and latitude, respectively. The regular grid system was employed in the filter, which has uniform angular spacing including the poles. The singularity at poles was eliminated by incorporating variable transforms and continuity-matching boundary conditions across poles. The high-order filter was assessed using the Rossby-Haurwitz wave, the observed geopotential, and observed wind field. The performance of the filter was found comparable to the filter based on the Galerkin procedure. The filter, employing the finite difference method, can be designed to give any target order of accuracy, which is an important advantage being unavailable in other methods. The computational complexity is represented with 2n-1 diagonal matrices solver with n being the target order of accuracy. Along with the availability of arbitrary target-order, it is also advantageous that the filter can adopt the reduced grid to increase computational efficiency.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2001.10a
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• pp.281-285
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• 2001

According to standard procedures as defined in the users handbook for sea level data processes, I was compared to Topex/poseidon sea level data from the first 350days of mission and Tide Gauge sea level data from the Amsterdam- Crozet- Kerguelen region in the South Indian Ocean. The comparison improves significantly when many factors for the corrections were removed, then only the aliased oceanic tidal energy is removed by oceanic tide model in this period. Making the corrections and smoothing the sea level data over 60km along-track segments and the Tide Gauge sea level data for the time series results in the digital correlation and RMS difference between the two data of c=-0.12 and rms=11.4cm, c=0.55 and rms=5.38cm, and c=0.83 and rms=2.83cm for the Amsterdam, Crozet and Kerguelen plateau, respectively. It was also found that the Kerguelen plateau has a comparisons due to propagating signals(the baroclinic Rossby wave with velocity of -3.9~-4.2cm/sec, period of 167days and amplitude of 10cm) that introduce temporal lags($\tau$=10~30days) between the altimeter and tide gauge time series. The conclusion is that on timescales longer than about 10days the RMS sea level errors are less than or of the order of several centimeters and are mainly due to the effects of currents rather than the effects of sterics(water temperature, density) and winds.

• Journal of the korean society of oceanography
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• v.31 no.4
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• pp.183-195
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• 1996

A barotropic non-linear numerical model is used to study the response of the Yellow Sea to winter cyclone passage. Cyclones normally come from the outside of the western boundary, China, and pass the region eastward. The cyclone parameters used for the present study are the following: the intensity, i.e., the maximum wind speed of the cyclone; the effective radius corresponding to this maximum; and the translation speed. The equations of motion are integrated over the depth which is supposed to be a constant. The Gaussian function is used to define the stream function of the wind. The following results have been found. A northward current is generated by the frontal part of the cyclone near the western boundary. After the cyclone leaves the sea area, a southward current is generated by the rear part of the cyclone. After that, a northward current is generated once again due to the westward propagating Rossby waves. The response of the sea to the cyclone passage is strongly influenced by a steady current when the steady current and the current due to the cyclone wind are of the same order. The steady current diminishes the sea response and reduces the speed of the southward current, and enhances the northward current speed. The intensity and the translation speed of a cyclone also influence the flow pattern significantly.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.562-570
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• 2003

This experimental study concerns the characteristics of vortex flow in a concentric annulus with a diameter ratio of 0.52, whose outer cylinder is stationary and inner one is rotating. Pressure losses and skin friction coefficients have been measured for fully developed flows of water and of 0.4% aqueous solution of sodium carboxymethyl cellulose (CMC), respectively, when the inner cylinder rotates at the speed of 0～600 rpm. Also, the visualization of vortex flows has been performed to observe the unstable waves. The results of present study reveal the relation of the bulk flow Reynolds number Re and Rossby number Ro with respect to the skin friction coefficients. In somehow, they show the existence of flow instability mechanism. The effect of rotation on the skin friction coefficient is significantly dependent on the flow regime. The change of skin friction coefficient corresponding to the variation of rotating speed is large for the laminar flow regime, whereas it becomes smaller as Re increases for the transitional flow regime and. then, it gradually approach to zero for the turbulent flow regime. Consequently, the critical (bulk flow) Reynolds number Re$\_$c/ decreases as the rotational speed increases. Thus, the rotation of the inner cylinder promotes the onset of transition due to the excitation of Taylor vortices.