Numerical Methods for Partial Differential Equations

Abstract

| References | Full Text: PDF (Size: 229K) Save Article Time-dependent algorithms for viscoelastic flow: Finite element/volume schemes (p 272-296) M. F. Webster, H. R. Tamaddon-Jahromi, M. Aboubacar Published Online: 13 Jul 2004 DOI: 10.1002/num.20037 Abstract | References | Full Text: PDF (Size: 873K) Save Article A posteriori error estimation and adaptive computation of viscoelastic fluid flow (p 297-322) Vincent J. Ervin, Louis N. Ntasin Published Online: 30 Jul 2004 DOI: 10.1002/num.20038 Abstract | References | Full Text: PDF (Size: 330K) Save Article An efficient numerical method for the resolution of the Kirchhoff-Love dynamic plate equation (p 323-348) Eliane Becache, Gregoire Derveaux, Patrick Joly Published Online: 30 Jul 2004 DOI: 10.1002/num.20041 Abstract | References | Full Text: PDF (Size: 268K) Save Article A mesh-free approach to solving the axisymmetric Poisson's equation (p 349-367) C. S. Chen, A. S. Muleshkov, M. A. Golberg, R. M. M. Mattheij Published Online: 6 Aug 2004 DOI: 10.1002/num.20040 Abstract | References | Full Text: PDF (Size: 144K) Save Article On the structure and growth rate of unstable modes to the Rossby-Haurwitz wave (p 368-386) Yuri N. Skiba, Ismael Perez-Garcia Published Online: 6 Aug 2004 DOI: 10.1002/num.20042 Abstract | References | Full Text: PDF (Size: 223K) Save Article Reliable, goal-oriented postprocessing for FE-discretizations (p 387-396) F. T. Suttmeier Published Online: 17 Aug 2004 DOI: 10.1002/num.20046 Abstract | References | Full Text: PDF (Size: 205K) Save Article An immersed interface method for anisotropic elliptic problems on irregular domains in 2D (p 397-420) Miguel A. Dumett, James P. Keener Published Online: 1 Sep 2004 DOI: 10.1002/num.20051 Abstract | References | Full Text: PDF (Size: 418K) Save Article On the Structure and Growth Rate of Unstable Modes to the Rossby-Haurwitz Wave Yuri N. Skiba, Ismael Perez-Garcia Centro de Ciencias de la Atmosfera, Universidad Nacional Autonoma de Mexico, Circuito Exterior, CU, C.P. 04510, Mexico, D.F., Mexico Received 13 May 2004; accepted 18 May 2004 Published online 6 August 2004 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.20042 The normal mode instability study of a steady Rossby-Haurwitz wave is considered both theoretically and numerically. This wave is exact solution of the nonlinear barotropic vorticity equation describing the dynamics of an ideal fluid on a rotating sphere, as well as the large-scale barotropic dynamics of the atmosphere. In this connection, the stability of the Rossby-Haurwitz wave is of considerable mathematical and meteorological interest. The structure of the spectrum of the linearized operator in case of an ideal fluid is studied. A conservation law for perturbations to the Rossby-Haurwitz wave is obtained and used to get a necessary condition for its exponential instability. The maximum growth rate of unstable modes is estimated. The orthogonality of the amplitude of a non-neutral or non-stationary mode to the RossbyHaurwitz wave is shown in two different inner products. The analytical results obtained are used to test and discuss the accuracy of a numerical spectral method used for the normal mode stability study of arbitrary flow on a sphere. The comparison of the numerical and theoretical results shows that the numerical instability study method works well in case of such smooth solutions as the zonal flows and RossbyHaurwitz waves. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 21: 368–386, 2005