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Stability of the Divergent Barotropic Rossby-Haurwitz Wave
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 Title & Authors
Stability of the Divergent Barotropic Rossby-Haurwitz Wave
Jeong, Han-Byeol; Cheong, Hyeong-Bin;
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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.
steady Rossby-Haurwitz wave;shallow waver model;Fourier-finite element method;spherical harmonics function;
 Cited by
Baines, P.G., 1976, The stability of planetary waves on a sphere. Journal of Fluid Mechanics, 73, 193-213. crossref(new window)

Browning, G.L., Hack, J.J., and Swarztrauber, P.N., 1989, A comparison of three numerical methods for solving differential equations on the sphere. Monthly Weather Review, 117, 1058-1075. crossref(new window)

Cheong, H.B., 2000, Application of double Fourier series to the Shallow-Water Equations on a Sphere. Journal of Computational Physics, 165, 261-287. crossref(new window)

Cheong, H.B., 2006, A dynamical core with double Fourier series: Comparison with the spherical harmonics method. Monthly Weather Review, 134, 1299-1315. crossref(new window)

Cheong, H.B. and Park, J.R., 2007, Geopotential field in nonlinear balance. Journal of Korean Earth Science Society, 28, 936-946. crossref(new window)

Cheong, H.B. and Jeong, H.B., 2015, Construction of the spherical high-order filter for applications to global meteorological data. Journal of Korean Earth Science Society, 36, 476-483. crossref(new window)

Cheong, H.B. and Kang, H.G., 2015, Eigensolutions of the spherical Laplacian for the cubed-sphere and icosahedral-hexagonal grids. Quarterly Journal of the Royal Meteorological Society, 141, 3383-3398. crossref(new window)

Cheong, H.B., Kong, H.J., Kang, H.G., and Lee, J.D., 2015, Fourier Finite-Element Method with Linear Basis Functions on a Sphere: Application to Elliptic and Transport Equations. Monthly Weather Review, 143, 1275-1294. crossref(new window)

Craig, R.A., 1945, A solution of the nonlinear vorticity equation for atmospheric motion. Journal of the Atmospheric Sciences, 2, 175?178.

Daley, R., 1983, Linear non-divergent mass-wind laws on the sphere. Tellus, 35A, 17-27. crossref(new window)

Haurwitz, B., 1940, The motion of atmospheric disturbances on a spherical earth. Journal of Marine Research, 3, 254-267.

Hoskins, B.J., 1973, Stability of the Rossby-Haurwitz wave. Quarterly Journal of the Royal Meteorological Society, 99, 723-745. crossref(new window)

Krishnamurti, T.N., Bedi, H.S., Hardiker, V.M., and Ramaswamy, L., 2006, An Introduction to Global Spectral Modeling. 2nd revised and enlarged ed. Springer, 317 pp

Longuet-Higgins, M.S., 1968, The Eigenfunctions of Laplace's tidal equations over a sphere. Philosophical Transactions of the Royal Society of London, Series A, 262, 511?607.

Lorenz, E.N., 1972, Barotropic instability of Rossby wave motion. Journal of Atmospheric Sciences, 29, 258-264

Lynch, P., 2009, On resonant Rossby-Haurwitz triads. Tellus, 61, 438-445. crossref(new window)

Neamtan, S.M., 1946, The motion of harmonic waves in the atmosphere. Journal of Meteorology, 3, 53?56. crossref(new window)

Orszag, S.A., 1970, Transform method for the calculation of vector-coupled sums: Application to the spectral form of the vorticity equation. Journal of Atmospheric Sciences, 27, 890-895. crossref(new window)

Ortland, D.A., 2005, Generalized Hough modes: The structure of damped global-scale waves propagating on a mean flow with horizontal and vertical shear. Journal of Atmospheric Sciences, 62, 2674-2683. crossref(new window)

Phillips, N.A., 1959, Numerical integration of the primitive equations on the hemisphere. Monthly Weather Review, 87, 333-345. crossref(new window)

Skiba, Y.N., 2008, Nonlinear and linear instability of the Rossby-Haurwitz wave. Journal of Mathematical Sciences, 149, 1708-1725. crossref(new window)

Swarztrauber, P.N., 1996, Spectral transform methods for solving the shallow-water equations on the sphere. Monthly Weather Review, 124, 730-744. crossref(new window)

Thuburn, J. and Li, Y., 2000, Numerical Simulations of Rossby-Haurwitz waves. Tellus, 52, 180-189.

Williamson, D.L. and Browning, G.L., 1973, Comparison of grids and difference approximations for numerical weather prediction over a sphere. Journal of Applied Meteorology, 12, 264-274. crossref(new window)

Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., and Swarztrauber, P.N., 1992, A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics, 102, 211-224. crossref(new window)