English
Internal wave dynamics in the atmosphere - Lecture 2
Multi angle
Auteurs : Klein, Rupert (Auteur de la Conférence)
CIRM (Editeur )
35Qxx - Equations of mathematical physics and other areas of application
86A35 - Atmospheric physics
35Q86 - PDEs in connection with geophysics
Ressources complémentaires :
http://smai.emath.fr/cemracs/cemracs19/resumesPDF/rupertklein.pdf
CIRM (Editeur )
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Résumé :
Earth's atmosphere hosts a rich spectrum of phenomena that involve interactions of a variety of processes across many length and time scales. A systematic approach to analyzing these scale dependent processes is a core task of theoretical meteorology and a prerequi- site to constructing reliable computational models for weather forecasting and climate simulation.
Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology.
Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations.
Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem.
Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.
Keywords : atmospheric physics; PDEs in connection with geophysics
Codes MSC : Lecture I The fundamental tools of similarity theory and formal single scale asymptotics will allow us to systematize the large zoo of scale-dependent model equations that one finds in modern textbooks of theoretical meteorology.
Lecture II The meteorological analogue of the incompressible flow equations are the ”anelastic” and ”pseudo-incompressible” models. Here we will learn how the presence of internal gravity waves in the atmosphere implies an asymptotic three-scale problem that renders the formal derivation and justification of these models much more intricate than the classical low Mach number derivation of the incompressible flow equations.
Lecture III The mechanisms by which tropical storms develop into hurricanes and typhoons are still under intense debate despite decades of research. A recent theory for the dynamics of strongly tilted atmospheric vortices will show how asymptotic methods help structuring this scientific debate, and how they offer new angles of scientific attack on the problem.
Lecture * If time permits, I will also summarize some ramifications of the scaling regimes and scaling theories considered in Lectures I-III on the construction of reliable computational methods.
Keywords : atmospheric physics; PDEs in connection with geophysics
35Qxx - Equations of mathematical physics and other areas of application
86A35 - Atmospheric physics
35Q86 - PDEs in connection with geophysics
Ressources complémentaires :
http://smai.emath.fr/cemracs/cemracs19/resumesPDF/rupertklein.pdf
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Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 30/08/2019 Date de captation : 17/07/2019 Sous collection : Research School arXiv category : Atmospheric and Oceanic Physics ; Fluid Dynamics Domaine : Mathematical Physics ; PDE Format : MP4 (.mp4) - HD Durée : 01:23:10 Audience : Researchers Download : https://videos.cirm-math.fr/2019-07-17_Klein_part2.mp4 
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Informations sur la Rencontre
Nom de la rencontre : CEMRACS : Geophysical Fluids, Gravity Flows / CEMRACS : Fluides géophysiques, écoulements gravitairesOrganisateurs de la rencontre : Duran, Arnaud ; Fabrèges, Benoit ; Lafitte, Pauline ; Lagoutière, Frédéric ; Marche, Fabien ; Rousset, Frédéric Dates : 15/07/2019 - 23/08/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/2084.html
Données de citation
DOI : 10.24350/CIRM.V.19548203Citer cette vidéo: Klein, Rupert (2019). Internal wave dynamics in the atmosphere - Lecture 2. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19548203 URI : http://dx.doi.org/10.24350/CIRM.V.19548203 |
Voir aussi
- [Multi angle] Asymptotic methods for the study of oceanographic models - Lecture 3: boundary layer methods / Auteur de la Conférence Dalibard, Anne-Laure.
- [Multi angle] Asymptotic methods for the study of oceanographic models - Lecture 2: filtering methods / Auteur de la Conférence Dalibard, Anne-Laure.
- [Multi angle] Asymptotic methods for the study of oceanographic models - Lecture 1: model hierarchy / Auteur de la Conférence Dalibard, Anne-Laure.
- [Multi angle] Modelling shallow water waves - Lecture 3 / Auteur de la Conférence Lannes, David.
- [Multi angle] Modelling shallow water waves - Lecture 2 / Auteur de la Conférence Lannes, David.
- [Multi angle] Modelling shallow water waves - Lecture 1 / Auteur de la Conférence Lannes, David.
- [Multi angle] Internal wave dynamics in the atmosphere, take-home messages - Lecture 3 / Auteur de la Conférence Klein, Rupert.
- [Multi angle] Scales in geophysical flows - Lecture 1 / Auteur de la Conférence Klein, Rupert.
- [Multi angle] Finite volume methods, dissipative problems and long time behavior - Part 3 : Finite volume methods and long time behavior / Auteur de la Conférence Chainais-Hillairet, Claire.
- [Multi angle] Finite volume methods, dissipative problems and long time behavior - Part 2 : Dissipative problems and long time behavior / Auteur de la Conférence Chainais-Hillairet, Claire.
- [Multi angle] Finite volume methods, dissipative problems and long time behavior - Part 1 : Introduction to the finite volume method / Auteur de la Conférence Chainais-Hillairet, Claire.
- [Multi angle] Nearshore hydrodynamics - Lecture 3 / Auteur de la Conférence Bonneton, Philippe.
- [Multi angle] Nearshore hydrodynamics - Lecture 2 / Auteur de la Conférence Bonneton, Philippe.
- [Multi angle] Nearshore hydrodynamics - Lecture 1 / Auteur de la Conférence Bonneton, Philippe.
- [Multi angle] How to extract information on geophysical mass movements from generated seismic waves? - Lecture 3 / Auteur de la Conférence Mangeney, Anne.
- [Multi angle] How to extract information on geophysical mass movements from generated seismic waves? - Lecture 2 / Auteur de la Conférence Mangeney, Anne.
- [Multi angle] How to extract information on geophysical mass movements from generated seismic waves? - Lecture 1 / Auteur de la Conférence Mangeney, Anne.
Bibliographie
- KLEIN, Rupert. Scale-dependent models for atmospheric flows. Annual review of fluid mechanics, 2010, vol. 42, p. 249-274. - https://doi.org/10.1146/annurev-fluid-121108-145537
- HUNDERTMARK, T. et REICH, S. A regularization approach for a vertical‐slice model and semi‐Lagrangian Störmer–Verlet time stepping. Quarterly Journal of the Royal Meteorological Society: A journal of the atmospheric sciences, applied meteorology and physical oceanography, 2007, vol. 133, no 627, p. 1575-1587. - https://doi.org/10.1002/qj.118
- KLEIN, Rupert. Asymptotics, structure, and integration of sound-proof atmospheric flow equations. Theoretical and Computational Fluid Dynamics, 2009, vol. 23, no 3, p. 161-195. - https://doi.org/10.1007/s00162-009-0104-y
- KLEIN, Rupert, ACHATZ, Ulrich, BRESCH, Didier, et al. Regime of validity of soundproof atmospheric flow models. Journal of the Atmospheric Sciences, 2010, vol. 67, no 10, p. 3226-3237. - https://doi.org/10.1175/2010JAS3490.1
- ACHATZ, Ulrich, KLEIN, Rupert, et SENF, Fabian. Gravity waves, scale asymptotics and the pseudo-incompressible equations. Journal of Fluid Mechanics, 2010, vol. 663, p. 120-147. - https://doi.org/10.1017/S0022112010003411
- LIPPS, Franik B. et HEMLER, Richard S. A scale analysis of deep moist convection and some related numerical calculations. Journal of the Atmospheric Sciences, 1982, vol. 39, no 10, p. 2192-2210. - https://doi.org/10.1175/1520-0469(1982)039%3C2192:ASAODM%3E2.0.CO;2
- DURRAN, Dale R. Improving the anelastic approximation. Journal of the atmospheric sciences, 1989, vol. 46, no 11, p. 1453-1461. - https://doi.org/10.1175/1520-0469(1989)046%3C1453:ITAA%3E2.0.CO;2
- OGURA, Yoshimitsu et PHILLIPS, Norman A. Scale analysis of deep and shallow convection in the atmosphere. Journal of the atmospheric sciences, 1962, vol. 19, no 2, p. 173-179. - https://doi.org/10.1175/1520-0469(1962)019%3C0173:SAODAS%3E2.0.CO;2
- KLEIN, Rupert, ACHATZ, Ulrich, BRESCH, Didier, et al. Regime of validity of soundproof atmospheric flow models. Journal of the Atmospheric Sciences, 2010, vol. 67, no 10, p. 3226-3237. - https://doi.org/10.1175/2010JAS3490.1
- BENACCHIO, Tommaso, O'NEILL, Warren P., et KLEIN, Rupert. A blended soundproof-to-compressible numerical model for small-to mesoscale atmospheric dynamics. Monthly Weather Review, 2014, vol. 142, no 12, p. 4416-4438. - https://doi.org/10.1175/MWR-D-13-00384.1
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