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Modelling the Leipzig Wind Profile with a (k-ε) model

  • Hiraoka, H. (Division of Global Environment Engineering, Graduate School of Engineering, Kyoto University)
  • 발행 : 2001.12.25

초록

The Leipzig Wind Profile is generally known as a typical neutral planetary boundary layer flow. But it became clear from the present research that it was not completely neutral but weakly stable. We examined whether we could simulate the Leipzig Wind Profile by using a ($k-{\varepsilon}$) turbulence model including the equation of potential temperature. By solving analytically the Second Moment Closure Model under the assumption of local equilibrium and under the condition of a stratified flow, we expressed the turbulent diffusion coefficients (both momentum and thermal) as functions of flux Richardson number. Our ($k-{\varepsilon}$) turbulence model which included the equation of potential temperature and the turbulent diffusion coefficients varying with flux Richardson number reproduced the Leipzig Wind Profile.

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참고문헌

  1. Andren A. (1991), "A TKE-dissipation model for the atmospheric boundary layer", Boundary-Layer Meteorology, 25, 207-221.
  2. Apsley D.D. and Castro I.P. (1997), "A limited-length scale k-e model for the neutral and stably-stratified atmospheric boundary layer", Boundary-Layer Meteorology, 83, 75-98. https://doi.org/10.1023/A:1000252210512
  3. Blackadar A.K. (1962), "The vertical distribution of wind and turbulent exchange in a neutral atmosphere", J. Geophys. Res., 67, 3095-3102. https://doi.org/10.1029/JZ067i008p03095
  4. Detering H.W. and Etling D. (1985), "Application of the E-${\varepsilon}$ turbulence model to the atmospheric boundary layer", Boundary-Layer Meteorology, 33, 113-133. https://doi.org/10.1007/BF00123386
  5. Duynkerke P.G. (1988), "Application of the E-${\varepsilon}$ turbulence closure model to neutral and stable atmospheric boundary-layers", J. Atmos. Sci., 45, 865-880. https://doi.org/10.1175/1520-0469(1988)045<0865:AOTTCM>2.0.CO;2
  6. Ellison T.H. and Turner J.S. (1960), "Mixing of dense fluid in a turbulent pipe flow", J. Fluid Mech., 8, 514-544. https://doi.org/10.1017/S0022112060000773
  7. Garatt J.R. (1992), The Atmospheric Boundary Layer, Appendix 4, Cambridge Univ. Press.
  8. Launder B.E. (1975), "On the effects of a gravitational field on the turbulent transport of heat and momentum", J. Fluid Mech., 67, 569-581. https://doi.org/10.1017/S002211207500047X
  9. Launder B.E. (1989), "Phenomelogical modelling: Present .... and future ?", Lecture Notes in Physics, 357, 439-485, Springer-Verlarg.
  10. Lettau H. (1950), "A re-examination of 'Leipzig Wind Profile' considering some relations between wind and turbulence in the frictional layer", Tellus, 2, 125-239. https://doi.org/10.1111/j.2153-3490.1950.tb00321.x
  11. Lettau H. (1962), "Theoretical wind spirals in the boundary layer of a barotropic atmosphere", Beitr. Phys. Atmosph., 35, 195-212.
  12. Mellor G. and Yamada T. (1982), "Development of a turbulence closure model for geophysics fluid problems", Rev. Geophys. and Space Phys., 20, 851-875. https://doi.org/10.1029/RG020i004p00851
  13. Sorbjan Z. (1989), Structure of the Atmospheric Boundary Layer, p.54, Prentice Hall.
  14. Ueda H., Mitsumoto S. and Komori S. (1981), "Buoyancy effects on the turbulent transport processes in the lower atmosphere", Quart. J. R. Met. Soc., 107, 561-578. https://doi.org/10.1002/qj.49710745307
  15. Xu, D. and Taylor P.A. (1997a), "An E-${\varepsilon}$-l turbulence closure scheme for planetary boundary-layer models: The neutrally stratified case", Boundary-Layer Meteorology, 84, 247-266. https://doi.org/10.1023/A:1000492827033
  16. Xu, D. and Taylor P.A. (1997b), "An E-${\varepsilon}$-l turbulence closure scheme for planetary boundary-layer models: Neutral stratification", Boundary-Layer Meteorology, 84, 267-287. https://doi.org/10.1023/A:1000404309286
  17. Yamada T. (1975), "The critical Richardson number and the ratio of the eddy transport coefficients obtained from a turbulence closure model", J. Atmos. Sci., 32, 926-933. https://doi.org/10.1175/1520-0469(1975)032<0926:TCRNAT>2.0.CO;2
  18. Yamada T. (1983), "Simulations of nocturnal drainage flows by a q2l turbulence closure model", J. Atmos. Sci., 40, 91-106. https://doi.org/10.1175/1520-0469(1983)040<0091:SONDFB>2.0.CO;2