Browse > Article
http://dx.doi.org/10.5467/JKESS.2016.37.2.107

Stability of the Divergent Barotropic Rossby-Haurwitz Wave  

Jeong, Han-Byeol (Department of Environmental Atmospheric Sciences, Pukyong National University)
Cheong, Hyeong-Bin (Department of Environmental Atmospheric Sciences, Pukyong National University)
Publication Information
Journal of the Korean earth science society / v.37, no.2, 2016 , pp. 107-116 More about this Journal
Abstract
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.
Keywords
steady Rossby-Haurwitz wave; shallow waver model; Fourier-finite element method; spherical harmonics function;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Hoskins, B.J., 1973, Stability of the Rossby-Haurwitz wave. Quarterly Journal of the Royal Meteorological Society, 99, 723-745.   DOI
2 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
3 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.
4 Lorenz, E.N., 1972, Barotropic instability of Rossby wave motion. Journal of Atmospheric Sciences, 29, 258-264
5 Lynch, P., 2009, On resonant Rossby-Haurwitz triads. Tellus, 61, 438-445.   DOI
6 Neamtan, S.M., 1946, The motion of harmonic waves in the atmosphere. Journal of Meteorology, 3, 53?56.   DOI
7 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.   DOI
8 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.   DOI
9 Phillips, N.A., 1959, Numerical integration of the primitive equations on the hemisphere. Monthly Weather Review, 87, 333-345.   DOI
10 Skiba, Y.N., 2008, Nonlinear and linear instability of the Rossby-Haurwitz wave. Journal of Mathematical Sciences, 149, 1708-1725.   DOI
11 Swarztrauber, P.N., 1996, Spectral transform methods for solving the shallow-water equations on the sphere. Monthly Weather Review, 124, 730-744.   DOI
12 Thuburn, J. and Li, Y., 2000, Numerical Simulations of Rossby-Haurwitz waves. Tellus, 52, 180-189.
13 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.   DOI
14 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.   DOI
15 Baines, P.G., 1976, The stability of planetary waves on a sphere. Journal of Fluid Mechanics, 73, 193-213.   DOI
16 Cheong, H.B. and Park, J.R., 2007, Geopotential field in nonlinear balance. Journal of Korean Earth Science Society, 28, 936-946.   DOI
17 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.   DOI
18 Cheong, H.B., 2000, Application of double Fourier series to the Shallow-Water Equations on a Sphere. Journal of Computational Physics, 165, 261-287.   DOI
19 Cheong, H.B., 2006, A dynamical core with double Fourier series: Comparison with the spherical harmonics method. Monthly Weather Review, 134, 1299-1315.   DOI
20 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.   DOI
21 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.   DOI
22 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.   DOI
23 Craig, R.A., 1945, A solution of the nonlinear vorticity equation for atmospheric motion. Journal of the Atmospheric Sciences, 2, 175?178.
24 Daley, R., 1983, Linear non-divergent mass-wind laws on the sphere. Tellus, 35A, 17-27.   DOI
25 Haurwitz, B., 1940, The motion of atmospheric disturbances on a spherical earth. Journal of Marine Research, 3, 254-267.