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Topics in Hyposonic Flow Theory pp 163–228Cite as

Slow Atmospheric Motion as a Low-Mach-Number Flow

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Part of the book series: Lecture Notes in Physics ((LNP,volume 672))

Abstract

First, in Sect. 6.1, we discuss in detail various facets of the applicability of the Boussinesq approximation to slow atmospheric motion. In Sect. 6.2, we give an asymptotic derivation of the Boussinesq lee-wave-model inviscid equations, from the system of Euler equations (1.40) derived in Sect. 1.7.1.

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References

  • H. Ashley and M. T. Landahl, Aerodynamics of Wings and Bodies Addison-Wesley, 1965.

    Google Scholar 

  • G. K. Batchelor. Q. J. Roy. Meteorol. Soc., 79 (1953), 224-235.

    Article  ADS  Google Scholar 

  • H. B´enard. Rev. G´en. Sci. Pures Appl., 11 (1900), 1261-1271.

    Google Scholar 

  • P. A. Bois. J. de M´ecanique, 15 (1976), 781-811.

    ADS  MATH  MathSciNet  Google Scholar 

  • P. A. Bois. J. de M´ecanique, 18 (1979), 395-417.

    Google Scholar 

  • P. A. Bois. Geophys. Astrophys. Fluid Dyn., 29 (1984), 267-303.

    Google Scholar 

  • A. J. Bourgeois and J. T. Beale. SIAM J. Math. Anal., 25(4) (1994), 1023-1068.

    Article  MathSciNet  MATH  Google Scholar 

  • J. Boussinesq, Th´eorie Analytique de la Chaleur, Vol. 2. Gauthier-Villars, Paris, 1903.

    Google Scholar 

  • S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability. Clarendon press, Oxford, 1961.

    MATH  Google Scholar 

  • J. G. Charney. Tellus, 7 (1955), 22.

    Article  MathSciNet  ADS  Google Scholar 

  • J. G. Charney. In: Procedings of the International Symposium on Numerical Weather Prediction, Tokyo, Novemver 1960, edited by. Meteorological Society of Japan, Tokyo, 1962 p. 131.

    Google Scholar 

  • P. G. Drazin. Tellus, 13 (1961), 239-251.

    Article  ADS  Google Scholar 

  • P. G. Drazin and W. H. Reid, Hydrodynamic Stability Cambridge University Press, Cambridge, 1981.

    MATH  Google Scholar 

  • J. A. Dutton and G. H. Fichtl. J. Atmosph. Sci., 26 (1969), 241.

    Article  ADS  Google Scholar 

  • C. Eckart and H. G. Ferris. Rev. Mod. Phys. 28(1) (1956), 48-52.

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • M. El Mabrouk and R. Kh.Zeytounian, Sur les conditions au bord pour equations primitives. Rev. Roumaine Math. Pures Appl. 29(3) (1984), 235-238.

    MathSciNet  MATH  Google Scholar 

  • B. L. Gavrilin. Izv. Akad. Nauk SSSR, Ser. Fiz. Atmos. Okean, 1 (1965), 557.

    Google Scholar 

  • P. Germain, M´ecanique, vol. 2. Ellipses, Palaiseau, 1986.

    Google Scholar 

  • H. P. Greenspan, The Theory of Rotating Fluids. Cambridge University Press, Cambridge, 1968.

    MATH  Google Scholar 

  • J. P. Guiraud, Examples ofApplications of Asymptotic Techniques to the Derivation of Models for Atmospheric Flows Advanced School coordinated by R. Kh. Zeytounian, CISM, Von Karman Session, 3-5 October 1983, Udine, Italy, unpublished notes, LMM, University of Paris VI.

    Google Scholar 

  • J. P. Guiraud and R. Kh. Zeytounian, A note on the asymptotic interpretation of the classical theory of lee waves in the troposphere and the role of the upper boundary condition. Geophys. Astrophys. Fluid Dyn. 12(1/2) (1979), 61-72.

    Article  MATH  ADS  Google Scholar 

  • J. P. Guiraud and R. Kh. Zeytounian, Asymptotic derivation of the ageostrophic model for atmospheric hydrostatic flows. Geophys. Astrophys. Fluid Dyn. 15(3$+$4) (1980), 283-295.

    Article  MATH  ADS  Google Scholar 

  • J. P. Guiraud and R. Kh. Zeytounian, Note on the adjustment to hydrostatic balance. Tellus, 34(1) (1982), 50-54.

    Article  ADS  Google Scholar 

  • J. C. R. Hunt and W. H. Snyder. J. Fluid Mech., 96(4) (1980), 671.

    Article  ADS  Google Scholar 

  • D. D. Joseph, Stability of Fluid Motions Vol. 2. Springer, Heidelberg, 1976.

    Google Scholar 

  • I. A. Kibel. Izv. Akad. Nauk. SSSR, Ser. Geograph. Geophys., No. 5 (1940), 627-638.

    Google Scholar 

  • I. A. Kibel, Vevedeniy´ev guidrodinamitcheskiye metodey kratkosrochnovo prognoza pogodey Gos Isd Tekh-Teor Literatour´e, Moscow, 1957. (English edition): An Introduction to the Hydrodynamical Methods of Short Period Weather Forecasting Macmillan, London, 1963.)

    Google Scholar 

  • I. A. Kibel, Hydrodynamical (numerical) short-range weather prediction. In: Mechanics in the USSR During the Last 50 Years (1917-1967) Vol. 2: Fluids and Gases, Mechanics edited by Nauka, Moscow, 1970, pp. 661-683.

    Google Scholar 

  • I. A. Kibel, Selected Works on Dynamical Meteorology Hydrometeo-Izdat, Leningrad, 1984.

    Google Scholar 

  • N. E. Kotchin, I. A. Kibel and N. V. Roze, Teoretitcheskaya Guidromekhanika Part 1, 6th edition. FM, Moscow, 1963.

    Google Scholar 

  • V. N. Kozhevnikov. Izv. Akad. Nauk SSSR, Ser. Geofiz. 7 (1963), 1108-1116.

    Google Scholar 

  • V. N. Kozhevnikov, Izv. Akad. Nauk SSSR, Atmosph. Ocean. Phys. 4(1) (1968), 16-27.

    MathSciNet  Google Scholar 

  • L. D. Landau and E. M. Lifshitz,Guidrodinamika 4th edition. Teoretitcheskaya Fizika, Vol. 6, Nauka, Moscow, 1988.

    Google Scholar 

  • J. L. Lions, R. Temam and S. Wang. Topol. Methods Nonlinear Anal., 4 (1994), 253-287.

    MathSciNet  MATH  ADS  Google Scholar 

  • R. Long. Tellus. 5 (1953), 42-57.

    Article  MathSciNet  ADS  Google Scholar 

  • W. V. R. Malkus, Boussinesq equations. In: Geophysical Fluid Dynamics Vol.~1, edited by Woods Hole Oceanographic Institution, Woods Hole, MA, 1964, pp. 1-12.

    Google Scholar 

  • L. Mahrt. J. Atmosph. Sci. 43(10) (1986), 1036-1044.

    Article  ADS  Google Scholar 

  • J. Mihaljan. Astrophys. J., 136 (1962), 1126.

    Article  ADS  MathSciNet  Google Scholar 

  • J. W. Miles. J. Fluid Mech., 33(4) (1968), 803-814.

    Article  ADS  MATH  Google Scholar 

  • A. S. Monin. Izv. Akad. Nauk SSSR, Ser. Geofiz., 4 (1958), 497.

    MathSciNet  Google Scholar 

  • A. S. Monin. Izv. Akad. Nauk SSSR, Ser. Geofiz., 7 (1961), 602.

    MathSciNet  Google Scholar 

  • A. S. Monin, Weather Forecasting as a Problem in Physics MIT Press, Cambridge, MA, 1972.

    Google Scholar 

  • A. S. Monin, Fundamentals of Geophysical Fluid Dynamics Hydrometeo-Izdat, Leningrad, 1988.

    Google Scholar 

  • J. Norbury and I. Roulstone (eds.), Large-Scale Amospheric-Ocean Dynamics Vol. 1, Analytical Methods and Numerical Models; Vol. 2, Geometric Methods and Models Cambridge University Press, Cambridge, 2002.

    Google Scholar 

  • A. Oberbeck. Ann. Phys. Chem., Neue Folge, 7 (1879), 271-292.

    Article  MATH  ADS  Google Scholar 

  • Y. Ogura and N. A. Phillips, J. Atmosph. Sci., 19 (1962), 173-179.

    Article  ADS  Google Scholar 

  • Ye. M. Pekelis. Bull. (Izv.) Acad. Sci. USSR, Atmosph. Ocean. Phys. 12(5) (1976), 470-477.

    Google Scholar 

  • R. Perez Gordon and M. G. Velarde, J. de Physique, 36 (7-8) (1979), 591-601.

    Article  ADS  Google Scholar 

  • R. Perez Gordon and M. G. Velarde, J. de Physique, 37(3) (1976), 177-182.

    Article  Google Scholar 

  • N. A. Phillips, Models for weather prediction. Annu. Rev. Fluid Mech., 2 (1970), 251-292.

    Article  ADS  Google Scholar 

  • O. M. Phillips, The Dynamics of the Upper Ocean 2nd edition. Cambridge University Press, Cambridge, 1977. Lord Rayleigh. Philos. Mag., 32 (1916), 529-546.

    Google Scholar 

  • L. F. Richardson, Weather Prediction by Numerical Processes Cambridge University Press, Cambridge, 1922 (reprinted by Dover, New York, 1966).

    Google Scholar 

  • E. A. Spiegel and G. Veronis. Astrophys. J., 131 (1960), 442-447. (Correction, Astrophys. J., 135 (1960), 655-656).

    Google Scholar 

  • M. Van Dyke, Perturbation Methods in Fluid Mechanics Academic Press, New York, 1964.

    MATH  Google Scholar 

  • M. G. Velarde and R. Kh. Zeytounian, Interfacial Phenomena and the Marangoni Effect CISM Courses and Lectures, No. 428, Springer, Vienna, 2002.

    Google Scholar 

  • C. Wilcox, Scattering Theory for the d'Alembert Equation in Exterior Domain Lecture Notes in Mathematics, No. 442, Springer, Berlin, 1975.

    Google Scholar 

  • C.-S. Yih, Stratified Flows Academic Press, London, 1980.

    MATH  Google Scholar 

  • R. Kh. Zeytounian, Etude des ph´enomènes d'ondes dans les ´ecoulement stationnaires d'un fluide stratifi´e non visqueux ONERA, Chatillon, Publication No. 126, Febuary 1969. (English translation edited by A. McPherson, Royal Aircraft Establishment, Farnborough, Library Translation 1404, December 1969). See also R. Kh. Zeytounian, J. de M´ecanique, 8(1969), 239-263, and R. Kh. Zeytounian, J. de M´ecanique 8(1969), 335-355.

    Google Scholar 

  • R. Kh. Zeytounian. C. R. Acad.Sci. Paris, 274A (1972), 1056. R. Kh. Zeytounion. C. R. Acad. Sci. Paris, 274A (1972), 1413.

    Google Scholar 

  • R. Kh. Zeytounian. Arch. Mech. (Archiwum Mechaniki Stosowanej), 26(3) (1974), 499-509.

    MATH  Google Scholar 

  • R. Kh. Zeytounian, La M´et´eorologie du point de vue du M´ecanicien des Fluides. Fluid Dyn. Trans. Polish Acad. Sci. 8(1976), 289-352.

    Google Scholar 

  • R. Kh. Zeytounian, Izv. Acad. Sci. USSR, Atmosph. Ocean. Phys. 15(5) (1979), 498-507.

    MathSciNet  Google Scholar 

  • R. Kh. Zeytounian, Asymptotic Modeling of Atmospheric Flows Springer, Heidelberg, 1990.

    MATH  Google Scholar 

  • R. Kh. Zeytounian, Meteorological Fluid Dynamics. Lecture Notes in Physics, m5, Springer, Heidelberg, 1991.

    Google Scholar 

  • R. Kh. Zeytounian. Phys.-Uspekhi, 41(3) (1998), 241-267.

    Article  MathSciNet  ADS  Google Scholar 

  • R. Kh. Zeytounian, Theory and Applications of Nonviscous Fluid Flows Springer, Heidelberg, 2002a.

    MATH  Google Scholar 

  • R. Kh. Zeytounian, Asymptotic Modelling of Fluid Flow Phenomena Fluid Mechanics and Its Applications, vol. 64, series Ed. R. Moreau, Kluwer Academic, Dordrecht, 2002b.

    Google Scholar 

  • R. Kh. Zeytounian, On the foundations of the Boussinesq approximation applicable to atmospheric motions. Izv. Atmosph. Ocean. Phys., 39 Suppl. (2003), S1-S14.

    Google Scholar 

  • R. Kh. Zeytounian, Weather prediction as a problem in fluid dynamics (on the 100th birthday of I. A. Kibel). Izv. Atmosph. Ocean. Phys., 40(5) (2004), 527-539.

    MathSciNet  Google Scholar 

  • R. Kh. Zeytounian and J. P. Guiraud, Asymptotic features of low Mach number flows in aerodynamics and in the atmosphere. In: Advances in Computational Methods for Boundary and Interior Layers, BAIL III edited by J.~J.~H. Miller. Boole Press, Dublin, 1984, pp. 95-100.

    Google Scholar 

  • A. Zygmund, Trigonometric Series, 2nd edition. Cambridge University Press, New York, 1958.

    Google Scholar 

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  1. Department of Chemical Engineering, 12 Rue St Fiacre, 75002 Paris, France

    Professor Radyadour Kh. Zeytounian

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Kh. Zeytounian, R. Slow Atmospheric Motion as a Low-Mach-Number Flow. In: Topics in Hyposonic Flow Theory. Lecture Notes in Physics, vol 672. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11414346_6

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  • DOI: https://doi.org/10.1007/11414346_6

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  • Print ISBN: 978-3-540-25549-9

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