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자료유형
학술저널
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저널정보
한국기상학회 Asia-Pacific Journal of Atmospheric Sciences Asia-Pacific Journal of Atmospheric Sciences Vol.44 No.4
발행연도
2008.11
수록면
401 - 416 (16page)

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The height field, in balance with the Rossby-Haurwitz wave of the first antisymmetric mode with zonal wavenumber m on the inclined rotation axis, was obtained analytically for the super-rotating background state. The balanced height consists of six zonal wavenumber components of 1, 2, m-1, m, m+1, and 2m, along with the zonal-mean component. The zonal wavenumber components 1 and 2 among the six are found to be independent of the amplitude of the Rossby-Haurwitz wave. For the inclination angle of π / 2, the zonal wavenumber components of 1 and m disappear. Based on the Rossby-Haurwitz wave and associated balanced height, analytic forced solutions of the shallow water equations on the sphere with the topography are presented. The height field is forced by a steady or traveling forcing while the vorticity and the divergence equations are set free of the forcing. The forcing is designed in such a way that the height field can maintain a balanced state with the Rossby-Haurwitz wave by specifying the topography as an arbitrary function of the streamfunction. The forced wave, being free of divergence, propagates without changing shape with the angular velocity of the free Rossby-Haurwitz wave. The analytic forced solutions are applied to the spherical harmonics spectral model as the test methods to evaluate the numerical performance. In order to give more rigorous test on the pole problem associated with the spherical coordinates, the poleward rotation of the forced solutions through coordinate transform is introduced. The results of time integration with the initial condition of balanced state are compared to the analytic solutions for the resolution of 160×80, 320×160 and 640×320 transform grids. It was found that when the model resolution is fixed the error decreases as the zonal wavenumber of the forced wave increases due to the lower phase velocity for the higher wavenumber. For a fixed zonal wavenumber, however, the error exhibited little variation with the resolution because the forced solution is composed of only a single wavenumber component. It was shown that the error becomes smaller when the inclination angle of the rotation axis increases.
#Shallow Water Equations #Test Method #Spherical harmonics spectral model #Rossby-Haurwitz wave

목차

Abstract
1. Introduction
2. Shallow water equations and analytical forced solutions
3. Analytical solutions of shallow water equations with topographic forcing
4. Use of analytical solutions as test method
5. Summary and conclusions
REFERENCES

참고문헌 (19)

참고문헌 신청
1. [단행본] - Arfken, G. / 1985 / Mathematical methods for physicists.3rd Eds. / Academic Press : 985 ~ google schola 2. [학술지(정기간행물)] - Asselin, R. / 1972 / Frequency filter for time integrations / Mon. Wea. Rev 100 : 487 ~ 490 google schola 3. [학술지(정기간행물)] - Baines, P. G. / 1976 / The stability of planetary waves on asphere / J. Fluid Mech 73 : 193 ~ 213 google schola 4. [학술지(정기간행물)] - Browning, G. L. / 1989 / A comparison of three numerical methods for solvingdifferential equations on the sphere / Mon. Wea. Rev 117 : 1058 ~ 1075 google schola 5. [학술지(정기간행물)] - Cheong, H.‐B. / 2006 / A dynamical core with doubleFourier series: Comparison with the spherical harmonicsmethod / Mon. Wea. Rev 134 : 1299 ~ 1315 google schola

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