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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.
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참고문헌 (24)
참고문헌 신청
Baines, P. G. / 1976 / The stability of planetary waves on a sphere / J. Fluid Mechanics 73:193~213
Browning, G. L. / 1989 / A comparison of three numerical methods for solving differential equations on the sphere / Monthly Weather Review 117:1058~1075
Caflisch, R. E. / 1988 / Mathematical aspects of vortex dynamics, Edited / Proceedings of the workshop on mathematical aspects of vortex dynamics :233
Cheong, H. B. / 2006 / A dynamical core with double Fourier series: Comparison with the spherical harmonics method / Monthly Weather Review 134:1299~1315
정형빈 / 2014 / Construction of Orthogonal Basis Functions with Non-Divergent Barotropic Rossby-Haurwitz Waves / 한국지구과학회지 35(5):333~341
Browning, G. L. / 1989 / A comparison of three numerical methods for solving differential equations on the sphere / Monthly Weather Review 117:1058~1075
Caflisch, R. E. / 1988 / Mathematical aspects of vortex dynamics, Edited / Proceedings of the workshop on mathematical aspects of vortex dynamics :233
Cheong, H. B. / 2006 / A dynamical core with double Fourier series: Comparison with the spherical harmonics method / Monthly Weather Review 134:1299~1315
정형빈 / 2014 / Construction of Orthogonal Basis Functions with Non-Divergent Barotropic Rossby-Haurwitz Waves / 한국지구과학회지 35(5):333~341
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