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Geophysical and astrophysical fluid dynamics, Vol.70 No.1-4. The stability of barotropic vortices - implications for tropical cyclone motion / H. C. Weber
in Geophysical and astrophysical fluid dynamics
Titre de série : Geophysical and astrophysical fluid dynamics, Vol.70 No.1-4 Titre : The stability of barotropic vortices - implications for tropical cyclone motion Type de document : articles et extraits Auteurs : H. C. Weber, Auteur ; R. K. Smith, Auteur Année de publication : 1993 Importance : p.1-30 ISBN/ISSN/EAN : 0309-1929 Langues : Français (fre) Mots-clés : BAROTROPIC VORTICES MODEL SHALLOW WATER SHALLOW-WATER SHEAR-FLOW TROPICAL CYCLONES VORTEX Résumé : We investigate the existence of normal mode perturbations to barotropic vortices defined by tangential velocity profiles that have been used in recent studies of tropical cyclone motion. For this purpose we have developed a new procedure, more accurate than previous ones, to search systematically for the eigensolutions. Linear stability analyses are carried out both for vortices in a nondivergent barotropic model and for those in a shallow water model, in each case using cylindrical coordinates on an f-plane. The nondivergent barotropic vorticity equation is used to determine the normal modes of a range of continuous vortex profiles with zero relative circulation at infinity. All profiles were found to be stable at azimuthal wavenumber one, the neutral nonrotating mode found by Michalke and Timme (1967) being the only mode that exists. At higher wavenumbers no normal modes were found except for an unstable mode of wavenumber two for a profile used by Smith and Ulrich (1990) that decays relatively rapidly with radius. However, the growth rate of this mode is relatively small. Accordingly, our results justify an assumption made by Smith and Ulrich (1990) and Smith (1991) in the development of an analytic theory for tropical cyclone motion. Our analysis of the vortex profile of Chan and Williams (1987) and the discontinuous profiles of willoughby (1988) differs considerably from that of Peng and Williams (1991) who obtained eigenvalues that were strongly dependent on the radial resolution of their solution method. However, our results are qualitatively consistent, showing differences between 5% and 10%, with those of Gent and McWilliams (1986) for the range of profiles they studied. The shallow water model is applied to reexamine the stability of the Gaussian streamfunction profile studied by Flatau and Stevens (1989), a calculation of possible relevance to instabilities of the tropical cyclone outflow layer. Flatau and Stevens' model equations were found to be incomplete. When the terms missing from their equations are included, the results of the eigenfunction analysis are very different. In a control experiment using the incomplete equations, the results of Flatau and Stevens were qualitatively reproduced, but with quantitative differences up to 20%. Application of our method to the two vortex profiles studied by Willoughby (1990) gave quantitatively and qualitatively different results in comparison with Willoughby's findings. The implications of the existence of neutral or unstable normal modes for vortex motion in nondivergent barotropic models are discussed with reference to recent analytical studies of tropical cyclone motion. The existence of the nonrotating neutral wavenumber one mode in numerical vortex models is found to arise because of inaccuracy in the centre-location of the vortex in analogy with the results obtained by Sutyrin and Flierl (1991) for discontinuous vorticity profiles. The excitation of a wavenumber two mode produces no track deviation by nonlinear interaction in nondivergent barotropic models. Unstable and neutral wavenumber one modes that rotate were found only for the vortex profiles studied by Willoughby (1988, 1990). The excitation of such modes could be expected to lead to the cycloidal motion of such a vortex.
in Geophysical and astrophysical fluid dynamics
Geophysical and astrophysical fluid dynamics, Vol.70 No.1-4. The stability of barotropic vortices - implications for tropical cyclone motion [articles et extraits] / H. C. Weber, Auteur ; R. K. Smith, Auteur . - 1993 . - p.1-30.
ISSN : 0309-1929
Langues : Français (fre)
Mots-clés : BAROTROPIC VORTICES MODEL SHALLOW WATER SHALLOW-WATER SHEAR-FLOW TROPICAL CYCLONES VORTEX Résumé : We investigate the existence of normal mode perturbations to barotropic vortices defined by tangential velocity profiles that have been used in recent studies of tropical cyclone motion. For this purpose we have developed a new procedure, more accurate than previous ones, to search systematically for the eigensolutions. Linear stability analyses are carried out both for vortices in a nondivergent barotropic model and for those in a shallow water model, in each case using cylindrical coordinates on an f-plane. The nondivergent barotropic vorticity equation is used to determine the normal modes of a range of continuous vortex profiles with zero relative circulation at infinity. All profiles were found to be stable at azimuthal wavenumber one, the neutral nonrotating mode found by Michalke and Timme (1967) being the only mode that exists. At higher wavenumbers no normal modes were found except for an unstable mode of wavenumber two for a profile used by Smith and Ulrich (1990) that decays relatively rapidly with radius. However, the growth rate of this mode is relatively small. Accordingly, our results justify an assumption made by Smith and Ulrich (1990) and Smith (1991) in the development of an analytic theory for tropical cyclone motion. Our analysis of the vortex profile of Chan and Williams (1987) and the discontinuous profiles of willoughby (1988) differs considerably from that of Peng and Williams (1991) who obtained eigenvalues that were strongly dependent on the radial resolution of their solution method. However, our results are qualitatively consistent, showing differences between 5% and 10%, with those of Gent and McWilliams (1986) for the range of profiles they studied. The shallow water model is applied to reexamine the stability of the Gaussian streamfunction profile studied by Flatau and Stevens (1989), a calculation of possible relevance to instabilities of the tropical cyclone outflow layer. Flatau and Stevens' model equations were found to be incomplete. When the terms missing from their equations are included, the results of the eigenfunction analysis are very different. In a control experiment using the incomplete equations, the results of Flatau and Stevens were qualitatively reproduced, but with quantitative differences up to 20%. Application of our method to the two vortex profiles studied by Willoughby (1990) gave quantitatively and qualitatively different results in comparison with Willoughby's findings. The implications of the existence of neutral or unstable normal modes for vortex motion in nondivergent barotropic models are discussed with reference to recent analytical studies of tropical cyclone motion. The existence of the nonrotating neutral wavenumber one mode in numerical vortex models is found to arise because of inaccuracy in the centre-location of the vortex in analogy with the results obtained by Sutyrin and Flierl (1991) for discontinuous vorticity profiles. The excitation of a wavenumber two mode produces no track deviation by nonlinear interaction in nondivergent barotropic models. Unstable and neutral wavenumber one modes that rotate were found only for the vortex profiles studied by Willoughby (1988, 1990). The excitation of such modes could be expected to lead to the cycloidal motion of such a vortex.
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Code-barres Cote Support Localisation Section Disponibilité ART-7348-0 ART Document imprimé Bureau chercheur Bureau de LE DIZES Stéphane Disponible MODELE TRI-DIMENSIONNEL POUR LA SIMULATION NUMERIQUE DE LA COUCHE LIMITE PLANETAIRE : APPLICATION A LA COUCHE TROPICALE. / SOMMERIA-KLEIN G.
Titre : MODELE TRI-DIMENSIONNEL POUR LA SIMULATION NUMERIQUE DE LA COUCHE LIMITE PLANETAIRE : APPLICATION A LA COUCHE TROPICALE. Type de document : thèse Auteurs : SOMMERIA-KLEIN G., Auteur Année de publication : 1974 Langues : Français (fre) Mots-clés : ATMOSPHERE COUCHE LIMITE PLANETAIRE COUCHE LIMITE TROPICALE SIMULATION NUMERIQUE Note de contenu : Spécialité :
Thèse de Doctorat d'Etat es-Sciences Physique de l'Université Paris VI.
MODELE TRI-DIMENSIONNEL POUR LA SIMULATION NUMERIQUE DE LA COUCHE LIMITE PLANETAIRE : APPLICATION A LA COUCHE TROPICALE. [thèse] / SOMMERIA-KLEIN G., Auteur . - 1974.
Langues : Français (fre)
Mots-clés : ATMOSPHERE COUCHE LIMITE PLANETAIRE COUCHE LIMITE TROPICALE SIMULATION NUMERIQUE Note de contenu : Spécialité :
Thèse de Doctorat d'Etat es-Sciences Physique de l'Université Paris VI.
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Code-barres Cote Support Localisation Section Disponibilité TH0340 1974 SOM Document imprimé IRPHE Salle du conseil Disponible