Abstract
With emphasis on meteorological applications, we discuss here the fluid dynamical fundamental governing equations, their nondimensionalization including the identification of key nondimensional parameters, and a general approach to meteorological modelling based on multiple scales asymptotics.
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Bibliography
G. I. Barenblatt. Scaling, self-similarity, and intermediate asymptotics. Cambridge Texts in Applied Mathematics. Cambridge University Press, Cambridge, New York, Melbourne, 1996.
J.A. Biello and A.J. Majda. Transformations for temperature flux in multiscale models of the tropics. Theor. Comp. Fluid Dyn., under revision, 2006.
O. Forster. Analysis 3. Vieweg & Sohn Verlagsgesellschaft, Braunschweig, Wiesbaden, 3. edition, 1984.
D. M. W. Frierson. Midlatitude static stability in simple and comprehensive general circulation models. J. Atmos. Sci., 65:1049–1062, 2008.
A.E. Gill. Atmosphere-Ocean Dynamics, volume 30 of International geophysics series. Academic Press, New York, 1982.
H. Görtler. Dimensionsanalyse: Theorie der physikalischen Dimensionen mit Anwendungen. Ingenieurwissenschaftliche Bibliothek. Springer, Berlin, Heidelberg, New York, 1975.
J.B. Keller and L. Ting. Approximate equations for large scale atmospheric motions. Internal Report, http://www.arxiv.org/abs/physics/0606114, Inst. for Mathematics & Mechanics (renamed to Courant Institute of Mathematical Sciences in 1962), NYU, 1951.
J. Kevorkian and J.D. Cole. Multiple Scale and Singular Perturbation Methods, volume 114 of Applied Mathematical Sciences. Springer-Verlag, New York, 1996.
R. Klein. An applied mathematical view of meteorological modelling. In Applied Mathematics Entering the 21st century; Invited talks from the ICIAM 2003 Congress, volume 116. SIAM Proceedings in Applied Mathematics, 2004.
R. Klein. Multiple spacial scales in engineering and atmospheric low mach number flows. ESAIM: Math. Mod. & Num. Analysis (M2AN), 39:537–559, 2005.
R. Klein. Scale-dependent models for atmospheric flows. Ann. Rev. Fluid Mech., 42:249–274, 2010.
R. Klein and A.J. Majda. Systematic multiscale models for deep convection on mesoscales. Theor. Comp. Fluid Dyn., accepted, 2006.
R. Klein, E. Mikusky, and A. Owinoh. Multiple scales asymptotics for atmospheric flows. In A. Laptev, editor, 4th European Conference of Mathematics, Stockholm, Sweden, pages 201–220. European Mathematical Society Publishing House, 2004.
D. Kröner. Numerical Schemes for Conservation Laws. J. Wiley & Sons und B.G. Teubner-Verlag, Chichester, Stuttgart, 1997.
R.J. LeVeque. Numerical Methods for Conservation Laws. Lectures in Mathematics, ETH Zürich. Birkhäuser Verlag, Basel, Boston, Berlin, 1990.
A. J. Majda and R. Klein. Systematic multiscale models for the tropics. Journal of the Atmospheric Sciences, 60(2):393–408, 2003.
A.J. Majda and J.A. Biello. A multiscale model for tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. USA, 101:4736–4741, 2004.
E. Mikusky, A. Owinoh, and R. Klein. On the influence of diabatic effects on the motion of 3D-mesoscale vortices within a baroclinic shear flow. In Computational Fluid and Solid Mechanics 2005, pages 766–768. Elsevier, Amsterdam, 2005.
J. Pedlosky. Geophysical Fluid Dynamics. Springer-Verlag, New York, 2. edition, 1987.
T. Schneider. The general circulation of the atmosphere. Ann. Rev. Earth Planet. Sci., 34:655–688, 2006.
W. Schneider. Mathematische Methoden der Strömungsmechanik. Vieweg & Sohn Verlagsgesellschaft, Braunschweig, 1978.
R. Temam and A. Miranville. Mathematical Modeling in Continuum Mechanics. Cambridge University Press, Cambridge, UK, 2000.
W. Walter. Gewöhnliche Differentialgleichungen. Springer-Verlag, Berlin, Heidelberg, New York, 6. edition, 1996.
D. Werner. Funktionalanalysis. Springer-Verlag, Berlin, Heidelberg, New York, 3rd edition, 2000.
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Klein, R., Vater, S., Paeschke, E., Ruprecht, D. (2010). Multiple scales methods in meteorology. In: Steinrück, H. (eds) Asymptotic Methods in Fluid Mechanics: Survey and Recent Advances. CISM Courses and Lectures, vol 523. Springer, Vienna. https://doi.org/10.1007/978-3-7091-0408-8_5
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DOI: https://doi.org/10.1007/978-3-7091-0408-8_5
Publisher Name: Springer, Vienna
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