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Consideration for the tropopause’s displacements in the problem of flow over mountains

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Abstract

Within the framework of a two-dimensional, inviscid, stationary model, the problem of an unbounded (in height) two-layer quasi-static airflow over mesoscale mountains is considered. The airflow is characterized by a constant velocity and a discontinuity of temperature stratification at the inner interface (tropopause). The conjugation conditions for the flow fields at the boundary between the layers are formulated exactly, without the standard assumption of small perturbations. According to calculations, partial reflection of wave energy from the tropopause is substantially controlled by nonlinear effects associated with a finite height and shape of terrain. The tropopause’s displacement from the initial (equilibrium) level has a stabilizing effect on the flow, thus interfering with the development of anomalously strong disturbances. As a result, the flow field remains statically stable within a considerably wider range of flow parameters and for a larger mountain heights than predicted in the context of the conventional linear theory. The results obtained in this study are indicative of the importance of a correct consideration of the dynamic interaction between the troposphere and the overlying layers during both simulation of the process of flow and analysis of real atmospheric situations over mountains.

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References

  1. P. Queney, G. A. Corby, N. Gerbier, et al., The Airflow over Mountains, Ed. by M. A. Alaka (WMO, Geneva, 1960).

    Google Scholar 

  2. V. N. Kozhevnikov, Disturbances of the Atmosphere during Flow over Mountains (Nauchnyi Mir, Moscow, 1999) [in Russian].

    Google Scholar 

  3. A. Eliassen and E. Palm, “On the Transfer of Energy in Stationary Mountain Waves,” Geophys. Publ 22(3), 1–23 (1961).

    Google Scholar 

  4. W. Blumen, “A Random Model of Momentum Flux by Mountain Waves,” Geophys. Publ. 26(2), 1–33 (1965).

    Google Scholar 

  5. J. Klemp, D. K. Lilly “The Dynamics of Wave-Induced Downslope Winds,” J. Atmos. Sci. 32, 320–339 (1975).

    Article  Google Scholar 

  6. K. B. Moiseenko, “On the Role of the Stratosphere in the Process of Overflow of Mesoscale Mountains,” Ann. Geophys., No. 11, 3407–3417 (2005).

    Google Scholar 

  7. E. Gossard and W. Hooke, Waves in the Atmosphere (Elsevier, Amsterdam, 1975; Mir, Moscow, 1978).

    Google Scholar 

  8. R. B. Smith, “The Influence of Mountains on the Atmosphere,” Adv. Geophys. 21(1), 81–230 (1979).

    Google Scholar 

  9. E. Palm and A. Foldvik, “Contribution to the Theory of Two-Dimensional Mountain Waves,” Geophys. Publ. 21(6), 1–30 (1960).

    Google Scholar 

  10. F. H. Berkshire and F. W. G. Warren, “Some Aspects of Linear Lee Wave Theory for the Stratosphere,” Q. J. R. Meteorol. Soc. 96(407), 50–67 (1970).

    Article  Google Scholar 

  11. F. H. Berkshire, “Two-Dimensional Linear Lee Wave Modes for Models Including a Stratosphere,” Q. J. R. Meteorol. Soc. 101(428), 259–266 (1975).

    Article  Google Scholar 

  12. D. R. Durran, “Another Look on Downslope Windstorms. Part I: The Development of Analogs to Super-Critical Flow in an Infinitely Deep, Continuously Stratified Flow,” J. Atmos. Sci. 43, 2527–2543 (1986).

    Article  Google Scholar 

  13. D. R. Durran, “Mountain Waves and Downslope Winds,” in Atmospheric Processes over Complex Terrain, Ed. by W. D. Blumen (Am. Meteorol. Soc., Meteorol. Monograph, 1990), No. 45, pp. 59–81.

    Google Scholar 

  14. D. K. Lilly, “A Severe Downslope Windstorm and Aircraft Turbulence Event Induced by a Mountain Wave,” J. Atmos. Sci. 35, 59–77 (1978).

    Article  Google Scholar 

  15. V. N. Kozhevnikov and M. K. Bedanokov, “Wave Disturbances over the Crimean Mountains: Theory and Observations,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 34, 546–556 (1998) [Izv., Atmos. Ocean. Phys. 34, 491–500 (1998)].

    Google Scholar 

  16. R. B. Smith, “The Steeping of Hydrostatic Mountain Waves,” J. Atmos. Sci. 34, 1634–1654 (1977).

    Article  Google Scholar 

  17. J. L. Attié, A. Druilhet, P. Durand, and B. Bénech, “Two-Dimensional Structure of Mountain Wave Observed by Aircraft during the PYREX Experiment,” Ann. Geophys. 15, 823–839 (1997).

    Article  Google Scholar 

  18. D. K. Lilly and J. B. Klemp, “The Effects of Terrain Shape on Nonlinear Hydrostatic Mountain Waves,” J. Fluid Mech. 95, Part 2, 241–261 (1979).

    Article  Google Scholar 

  19. V. N. Kozhevnikov and K. B. Moiseenko, “Simulation of the Flow over a Mountain Ridge with Height-Varying Free-Stream Characteristics,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 40, 165–177 (2004) [Izv., Atmos. Ocean. Phys. 40, 142–152 (2004)].

    Google Scholar 

  20. R. R. Long, “Some Aspects of the Flow of Stratified Fluids. III. Continuous Density Gradients,” Tellus 7, 341–357 (1955).

    Article  Google Scholar 

  21. A. J. Claus, “Large-Amplitude Motion of a Compressible Fluid in the Atmosphere,” J. Fluid Mech. 19, Part 2, 267–289 (1963).

    Article  Google Scholar 

  22. V. N. Kozhevnikov and M. K. Bedanokov, “Nonlinear Multilayer Model of Flow over an Arbitrary Profile,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 29, 780–792 (1993).

    Google Scholar 

  23. N. E. Kochin, I. A. Kibel’, and N. V. Roze, Theoretical Fluid Mechanics, Part 1 (Fizmatgiz, Moscow, 1963) [in Russian].

    Google Scholar 

  24. G. Lyra, “Theorie Der Stationaren Leewellenstromung in Freien Atmosphare,” Z. Angew. Math. Mech. 23(1), 1–28 (1943).

    Google Scholar 

  25. J. W. Miles and H. E. Huppert, “Lee Waves in Stratified Flow. 4. Perturbation Approximations,” J. Fluid Mech. 35 Part 3, 497–525 (1969).

    Article  Google Scholar 

  26. L. N. Gutman, Introduction to the Theory of Mesometeorological Processes (Gidrometeoizdat, Leningrad, 1969) [in Russian].

    Google Scholar 

  27. D. K. Lilly, J. M. Nicholls, R. M. Chervin, et al., “Aircraft Measurements of Wave Momentum Flux over the Colorado Rocky Mountains,” Q. J. R. Meteorol. Soc. 108(457), 625–642 (1982).

    Article  Google Scholar 

  28. D. K. Lilly and J. P. Kennedy, “Observations of a Stationary Mountain Wave and Its Associated Momentum Flux and Energy Dissipation,” J. Atmos. Sci. 30, 1135–1152 (1973).

    Article  Google Scholar 

  29. N. I. Muskhelishvili, Singular Integral Equations (Fizmatgiz, Moscow, 1962) [in Russian].

    Google Scholar 

  30. M. Van Dyke, Perturbation Methods in Fluid Mechanics (Academic, New York, 1964).

    Google Scholar 

  31. V. N. Kozhevnikov, T. N. Bibikova, and E. V. Zhurba, “Orographic Disturbances of the Atmosphere over the Northern Ural,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 13, 451–461 (1977).

    Google Scholar 

  32. D. Lilly, Y. Pann, P. Kennedy, and W. Toutenhoofd, Data Catalog for the 1970 Colorado Lee Wave Observational Program (NCAR Tecnical Notes, Boulder, 1971), NCAR-TN/STR-72.

    Google Scholar 

  33. R. Scorer, Environmental Aerodynamics (Horwood, Chichester, 1978; Mir, Moscow, 1980).

    Google Scholar 

  34. N. E. Kochin, Effect of the Terrain Profile on Waves on the Interface between Two Masses of Fluids with Different Densities, Vol. 1 (Akad. Nauk SSSR, Moscow, 1949) [in Russian].

    Google Scholar 

  35. F. I. Frankl’ and L. N. Gutman, “Thermohydrodynamic Model of Bora,” Dokl. Akad. Nauk SSSR 130(3) (1960).

  36. A. A. Dorodnitsyn, “Effect of the Earth’s Surface Relief on Airflows,” Tr. TsIP, No. 21, 3–25 (1950).

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Original Russian Text © K.B. Moiseenko, 2007, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2007, Vol. 43, No. 2, pp. 182–192.

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Moiseenko, K.B. Consideration for the tropopause’s displacements in the problem of flow over mountains. Izv. Atmos. Ocean. Phys. 43, 158–167 (2007). https://doi.org/10.1134/S000143380702003X

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  • DOI: https://doi.org/10.1134/S000143380702003X

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