Multiple spatial scales in engineering and atmospheric low mach number flows

Mathematical Modelling and Numerical Analysis

Volumn 39, Issue 3, 2005, Pages 537-559

  Klein, Rupert ^a  

^a FREIE UNIVERSITÄT BERLIN   (Germany)

Author keywords

Atmospheric flows; Low Mach number flows; Multiple scales asymptotics

Indexed keywords

EID: 22144439741     PISSN: 0764583X     EISSN: None     Source Type: Journal    
DOI: 10.1051/m2an:2005022     Document Type: Conference Paper

References (40)

1. P.R. Bannon, On the anelastic approximation for a compressible atmosphere. J. Atmosphere Sci. 53 (1996) 3618-3628.
2. G.K. Batchelor, The conditions for dynamical similarity of motions of a frictionless perfect gas atmosphere. Quart. J. Roy. Meteorol. Soc. 79 (1953) 224-235.
3. J.R. Biello and A.J. Majda, A new multiscale model for the madden Julian oscillation. J. Atmosphere Sci. 62 (2005) in press.
4. N. Botta, R. Klein and A. Almgren, Asymptotic analysis of a dry atmosphere. ENUMATH, Jyväskylä, Finland (1999).
5. C. Bretherton and A. Sobel. The gill model and the weak temperature gradient (wtg) approximation. J. Atmosphere Sci. 60 (2003) 451-460.
6. J.G. Charney, A note on large-scale motions in the tropics. J. Atmosphere Sci. 20 (1963) 607-609.
7. S.B. Dorofeev, V.P. Sidorov, A.E. Dvoinishnikov and W. Breitung, Deflagration to detonation transition in large confined volume of lean hydrogen-air mixtures. Combustion & Flame 104 (1996) 95-110.
8. D.R. Durran, Improving the anelastic approximation. J. Atmosphere Sci. 46 (1989) 1453-1461.
9. A.E. Gill, Some simple solutions for heat-induced tropical circulation. Quart. J. Roy. Meteorol. Soc. 87 (1980) 447-462.
10. I.M. Held and B.J. Hoskins, Large-scale eddies and the general circulation of the troposphere. Adv. in Geophysics 28 (1985) 3-31.
11. J.C.R. Hunt, K.J. Richards and P.W.M. Brighton, Stably stratified shear flow over low hills. Quart. J. Roy. Meteorol. Soc. 114 (1988) 859-886.
12. R. Klein, Semi-implicit extension of a godunov-type scheme based on low mach number asymptotics I: One-dimensional flow. J. Comput. Phys. 121 (1995) 213-237.
13. R. Klein, Asymptotic analyses for atmospheric flows and the construction of asymptotically adaptive numerical methods. ZAMM 80 (2000) 765-777.
14. R. Klein, An applied mathematical view of theoretical meteorology, in Applied Mathematics Entering the 21st Century; Invited talks from the ICIAM 2003 Congress, SIAM Proceedings in Applied Mathematics 116 (2004).
15. R. Klein, Multiple scales asymptotics for atmospheric flows, in Proceedings of the 4th European Conference on Mathematics, Stockholm, Sweden (2004).
16. R. Klein and S. Vater, Mathematical modelling in climate research. Technical report, Freie Universität, Berlin, Germany (2005).
17. H. Lamb, Hydrodynamics. Dover Publishers, New York (1981).
18. F. Lipps and R. Hemler, A scale analysis of deep moist convection and some related numerical calculations. J. Atmosphere Sci. 39 (1982) 2192-2210.
19. F. Lipps and R. Hemler, Another look at the scale analysis of deep moist convection. J. Atmosphere Sci. 42 (1985) 1960-1964.
20. R. Madden and P. Julian, Description of global cell circulation cells in the tropics with a 40-50 day period. J. Atmosphere Sci. 29 (1972) 1109-1123.
21. A.J. Majda and J.A. Biello, A multiscale model for tropical intraseasonal oscillations. Proc. Natl. Acad. Sci. USA 101 (2004) 4736-4741.
22. A. Majda and R. Klein, Systematic multi-scale models for the tropics. J. Atmosphere Sci. 60 (2003) 393-408.
23. A. Majda and J. Sethian, The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Tech. 42 (1985) 185-205.
24. T. Matsuno, Quasi-geostrophic motions in the equatorial area. J. Meteorol. Soc. Jap. 44 (1966) 25-43.
25. T.M.J. Newley, H.J. Pearson and J.C.R. Hunt, Stably stratified rotating flow through a group of obstacles. Geophys. Astrophys. Fluid Dynam. 58 (1991) 147-171.
26. Y. Ogura and N.A. Phillips, Scale analysis of deep moist convection and some related numerical calculations. J. Atmosphere Sci. 19 (1962) 173-179.
27. J. Oliger and A. Sundstroem, Theoretical and practical aspects of some initial boundary value problems in fluid dynamics. NASA STI/Recon Technical Report N 77 25465 (November 1976).
28. J. Pedlosky, Ed., Geophysical Fluid Dynamics. Springer, Berlin, Heidelberg, New York, 2nd edition (1987).
29. V. Petoukhov, A. Ganopolski, V. Brovkin, M. Claussen, A. Eliseev, C. Kubatzki and S. Rahmstorf, Climber-2: A climate system model of intermediate complexity. Part I: Model description and performance for the present climate. Climate Dynamics 16 (2000) 1-17.
30. A.S. Worlikar and O.M. Knio, Numerical study of oscillatory flow and heat transfer in a loaded thermoacoustic stack. Numer. Heat Transfer 35 (1999) 49-65.
31. A.S. Worlikar, O.M. Knio and R. Klein, Numerical simulation of a thermoacoustic refrigerator. II: stratified flow around the stack. J. Comput. Fluids 144 (1998) 299-324.
32. Th. Schneider, N. Botta, R. Klein and K.J. Geratz, Extension of finite volume compressible flow solvers to multi-dimensional, variable density zero Mach number flow. J. Comput. Phys. 155 (1999) 248-286.
33. Th. Schneider, R. Klein, E. Besnoin and O. Knio, Computational analysis of a thermoacoustic refrigerator, in Proceedings of the joint EAA/ASA meeting (March 1999).
34. S. Schochet, The mathematical theory of low mach number flows. ESAIM: M2AN 39 (2005) 441-458.
35. V. Smiljanovski, V. Moser and R. Klein, A capturing-tracking hybrid scheme for deflagration discontinuities. J. Combustion Theory Modeling 1 (1997) 183-215.
36. A.A. Sobel, J. Nilsson and L. Polvani, The weak temperature gradient approximation and balanced tropical moisture waves. J. Atmosphere Sci. 58 (2001) 3650-3665.
37. P.J. Webster, Response of the tropical atmosphere to local steady forcing. Monthly Weather Review 100 (1972) 518-541.
38. A.A. White, A view of the equations of meteorological dynamics and various approximations, in Large Scale Atmosphere-Ocean Dynamics I: Analytical Methods and Numerical Models. J. Norbury and I. Roulstone, Eds., Cambridge University Press (2002).
39. G.B. Whitham, Linear and Non Linear Waves. John Wiley (1974).
40. R.K. Zeytounian, Meteorological Fluid Dynamics. Number m5 in Lecture Notes in Physics. Springer, Heidelberg, Berlin, New York (1991).