• Baldauf, M., and S. Brdar, 2016: 3D diffusion in terrain-following coordinates: Testing and stability of horizontally explicit, vertically implicit discretizations. Quart. J. Roy. Meteor. Soc., 142, 20872101, https://doi.org/10.1002/qj.2805.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Broad, A. S., 2002: Momentum flux due to trapped lee waves forced by mountains. Quart. J. Roy. Meteor. Soc., 128, 21672173, https://doi.org/10.1256/003590002320603593.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Clark, T. L., and W. R. Peltier, 1977: On the evolution and stability of finite amplitude mountain waves. J. Atmos. Sci., 34, 17151730, https://doi.org/10.1175/1520-0469(1977)034<1715:OTEASO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Clark, T. L., and R. D. Farley, 1984: Severe downslope wind storm calculations in two and three spatial dimensions using anelastic interactive grid nesting: A possible mechanism for gustiness. J. Atmos. Sci., 41, 329350, https://doi.org/10.1175/1520-0469(1984)041<0329:SDWCIT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Corby, G. A., and C. E. Wallington, 1956: Airflow over mountains: The lee-wave amplitude. Quart. J. Roy. Meteor. Soc., 82, 266274, https://doi.org/10.1002/qj.49708235303.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Dipankar, A., B. Stevens, R. Heinze, C. Moseley, G. Zängl, M. Giorgetta, and S. Brdar, 2015: Large eddy simulation using the general circulation model ICON. J. Adv. Model. Earth Syst., 7, 963986, https://doi.org/10.1002/2015MS000431.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and D. R. Durran, 2002: The dynamics of mountain-wave-induced rotors. J. Atmos. Sci., 59, 186201, https://doi.org/10.1175/1520-0469(2002)059<0186:TDOMWI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Doyle, J. D., and D. R. Durran, 2007: Rotor and subrotor dynamics in the lee of three-dimensional terrain. J. Atmos. Sci., 64, 42024221, https://doi.org/10.1175/2007JAS2352.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1986a: Another look at downslope windstorms. Part I: The development of analogs to supercritical flow in an infinitely deep, continuously stratified fluid. J. Atmos. Sci., 43, 25272543, https://doi.org/10.1175/1520-0469(1986)043<2527:ALADWP>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Durran, D. R., 1986b: Mountain waves. Mesoscale Meteorology and Forecasting, P. S. Ray, Ed., Amer. Meteor. Soc., 472–492.

    • Crossref
    • Export Citation
  • Durran, D. R., 1990: Mountain waves and downslope winds. Atmospheric Processes over Complex Terrain, Meteor. Monogr., No. 45, Amer. Meteor. Soc., 59–81.

    • Crossref
    • Export Citation
  • Eliassen, A., and E. Palm, 1960: On the transfer of energy in stationary mountain waves. Geophys. Publ., 22, 123.

  • Georgelin, M., E. Richard, and M. Petididier, 1996: The impact of diurnal cycle on a low-Froude number flow observed during the PYREX experiment. Mon. Wea. Rev., 124, 11191131, https://doi.org/10.1175/1520-0493(1996)124<1119:TIODCO>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gerbier, N., and M. Berenger, 1961: Experimental studies of lee waves in the French Alps. Quart. J. Roy. Meteor. Soc., 87, 1323, https://doi.org/10.1002/qj.49708737103.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Giorgetta, M. A., and Coauthors, 2018: ICON-A: The atmospheric component of the ICON Earth system model. Part I: Model description. J. Adv. Model. Earth Syst., 10, 16131637, https://doi.org/10.1029/2017MS001242.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Heinze, R., and Coauthors, 2017: Large-eddy simulations over Germany using ICON: A comprehensive evaluation. Quart. J. Roy. Meteor. Soc., 143, 69100, https://doi.org/10.1002/qj.2947.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Holmboe, J., and H. Klieforth, 1957: Investigations of mountain lee waves and airflow over the Sierra Nevada. University of California, Los Angeles, Dept. of Meteorology Rep., 290 pp.

    • Crossref
    • Export Citation
  • Inoue, M., G. Matheou, and J. Teixeira, 2014: LES of a spatially developing atmospheric boundary layer: Application of a fringe method for the stratocumulus to shallow cumulus cloud transition. Mon. Wea. Rev., 142, 34183424, https://doi.org/10.1175/MWR-D-13-00400.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, Q., and J. D. Doyle, 2008: On the diurnal variation of mountain waves. J. Atmos. Sci., 65, 13601377, https://doi.org/10.1175/2007JAS2460.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jiang, Q., J. D. Doyle, and R. B. Smith, 2006: Interaction between trapped waves and boundary layers. J. Atmos. Sci., 63, 617633, https://doi.org/10.1175/JAS3640.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., and D. R. Lilly, 1975: The dynamics of wave-induced downslope winds. J. Atmos. Sci., 32, 320339, https://doi.org/10.1175/1520-0469(1975)032<0320:TDOWID>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klemp, J. B., J. Dudhia, and A. D. Hassiotis, 2008: An upper gravity-wave absorbing layer for NWP applications. Mon. Wea. Rev., 136, 39874004, https://doi.org/10.1175/2008MWR2596.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klocke, D., M. Brueck, C. Hohenegger, and B. Stevens, 2017: Rediscovery of the doldrums in storm-resolving simulations over the tropical Atlantic. Nat. Geosci., 10, 891896, https://doi.org/10.1038/s41561-017-0005-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lilly, D. K., 1962: On the numerical simulation of buoyant convection. Tellus, 14, 148172, https://doi.org/10.3402/tellusa.v14i2.9537.

  • Lorenz, E. N., 1960: Energy and numerical weather prediction. Tellus, 12, 364373, https://doi.org/10.3402/tellusa.v12i4.9420.

  • Lott, F., 2007: The reflection of a stationary gravity wave by a viscous boundary layer. J. Atmos. Sci., 64, 33633371, https://doi.org/10.1175/JAS4020.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lott, F., 2016: A new theory for downslope windstorms and trapped mountain waves. J. Atmos. Sci., 73, 35853597, https://doi.org/10.1175/JAS-D-15-0342.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Munters, W., C. Meneveau, and J. Meyers, 2016: Turbulent inflow precursor method with time-varying direction for large-eddy simulations and applications to wind farms. Bound.-Layer Meteor., 159, 305328, https://doi.org/10.1007/s10546-016-0127-z.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Narcowich, F. J., and J. D. Ward, 1994: Generalized Hermite interpolation via matrix-valued conditionally positive definite functions. Math. Comput., 63, 661687, https://doi.org/10.1090/S0025-5718-1994-1254147-6.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ólafsson, H., and P. Bougeault, 1997: The effect of rotation and surface friction on orographic drag. J. Atmos. Sci., 54, 193210, https://doi.org/10.1175/1520-0469(1997)054<0193:TEORAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pearce, R. P., and P. W. White, 1967: Lee wave characteristics derived from a three-layer model. Quart. J. Roy. Meteor. Soc., 93, 155165, https://doi.org/10.1002/qj.49709339602.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Peltier, W. R., and J. F. Scinocca, 1990: The origin of severe downslope windstorm pulsations. J. Atmos. Sci., 47, 28532870, https://doi.org/10.1175/1520-0469(1990)047<2853:TOOSDW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Phillips, D. S., 1984: Analytical surface pressure and drag for linear hydrostatic flow over three-dimensional elliptical mountains. J. Atmos. Sci., 41, 10731084, https://doi.org/10.1175/1520-0469(1984)041<1073:ASPADF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Queney, P., G. A. Corby, N. Gerbier, H. Koschmieder, and J. Zierep, 1960: The airflow over mountains. WMO Tech. Note 34, 135 pp.

  • Ralph, F. M., P. J. Neiman, T. L . Keller, D. Levinson, and L. Fedor, 1997: Observations, simulations and analysis of nonstationary trapped lee waves. J. Atmos. Sci., 54, 13081333, https://doi.org/10.1175/1520-0469(1997)054<1308:OSAAON>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Reinecke, P. A., and D. R. Durran, 2008: Estimating topographic blocking using a Froude number when the static stability is nonuniform. J. Atmos. Sci., 65, 10351048, https://doi.org/10.1175/2007JAS2100.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sachsperger, J., S. Serafin, and V. Grubišić, 2015: Lee waves on the boundary-layer inversion and their dependence on free-atmospheric stability. Front. Earth Sci., 3, 70, https://doi.org/10.3389/feart.2015.00070.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sachsperger, J., S. Serafin V. Grubišić, I. Stiperski, and A. Paci, 2017: The amplitude of lee waves on the boundary-layer inversion. Quart. J. Roy. Meteor. Soc., 143, 2736, https://doi.org/10.1002/qj.2915.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sauer, J. A., D. Muñoz-Esparza, J. M. Canfield, K. R. Costigan, R. R. Linn, and Y. Kim, 2016: A large-eddy simulation study of atmospheric boundary layer influence on stratified flows over terrain. J. Atmos. Sci., 73, 26152632, https://doi.org/10.1175/JAS-D-15-0282.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sawyer, J. S., 1960: Numerical calculation of the displacements of a stratified airstream crossing a ridge of small height. Quart. J. Roy. Meteor. Soc., 86, 326345, https://doi.org/10.1002/qj.49708636905.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schiemann, R., D. Lüthi, and C. Schär, 2009: Seasonality and interannual variability of the westerly jet in the Tibetan Plateau region. J. Climate, 22, 29402957, https://doi.org/10.1175/2008JCLI2625.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scinocca, J., and W. Peltier, 1989: Pulsating downslope windstorms. J. Atmos. Sci., 46, 28852914, https://doi.org/10.1175/1520-0469(1989)046<2885:PDW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Scorer, R. S., 1949: Theory of waves in the lee of mountains. Quart. J. Roy. Meteor. Soc., 75, 4156, https://doi.org/10.1002/qj.49707532308.

  • Scorer, R. S., and H. Klieforth, 1959: Theory of mountain waves of large amplitude. Quart. J. Roy. Meteor. Soc., 85, 131143, https://doi.org/10.1002/qj.49708536406.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. B., S. Skubis, J. D. Doyle, A. S. Broad, C. Kiemle, and H. Volkert, 2002: Mountain waves over Mont Blanc: Influence of a stagnant boundary layer. J. Atmos. Sci., 59, 20732092, https://doi.org/10.1175/1520-0469(2002)059<2073:MWOMBI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. B., Q. Jiang, and J. D. Doyle, 2006: A theory of gravity wave absorption by a boundary layer. J. Atmos. Sci., 63, 774781, https://doi.org/10.1175/JAS3631.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Soufflet, C., F. Lott, and F. Damiens, 2019: Trapped mountain waves with a critical level just below the surface. Quart. J. Roy. Meteor. Soc., 145, 15031514, https://doi.org/10.1002/qj.3507.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A., J. L. Argaín, and P. M. Miranda, 2013: Orographic drag associated with lee waves trapped at an inversion. J. Atmos. Sci., 70, 29302947, https://doi.org/10.1175/JAS-D-12-0350.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Vosper, S. B., 2004: Inversion effects on mountain lee waves. Quart. J. Roy. Meteor. Soc., 130, 17231748, https://doi.org/10.1256/qj.03.63.

  • Xue, H., J. Li, T. Qian, and H. Gu, 2020: A 100-m-scale modeling study of a gale event on the lee side of a long narrow mountain. J. Appl. Meteor. Climatol., 59, 2345, https://doi.org/10.1175/JAMC-D-19-0066.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zang, Z.-L., and M. Zhang, 2008: A study of the environmental influence on the amplitude of lee waves. Adv. Atmos. Sci., 25, 474480, https://doi.org/10.1007/s00376-008-0474-x.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zang, Z.-L., M. Zhang, and H. Huang, 2007: Influence of the Scorer parameter profile on the wavelength of trapped lee waves. J. Hydrodyn., 19, 165172, https://doi.org/10.1016/S1001-6058(07)60044-4.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zängl, G., D. Reinert, P. Ripodas, and M. Baldauf, 2015: The ICON (Icosahedral Non-Hydrostatic) modelling framework of DWD and MPI-M: Description of the non-hydrostatic dynamical core. Quart. J. Roy. Meteor. Soc., 141, 563579, https://doi.org/10.1002/qj.2378.

    • Crossref
    • Search Google Scholar
    • Export Citation
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A Large-Eddy Simulation Study on the Diurnally Evolving Nonlinear Trapped Lee Waves over a Two-Dimensional Steep Mountain

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  • 1 State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing, China
  • 2 Max Planck Institute for Meteorology, Hamburg, Germany
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Abstract

The diurnally evolving trapped lee wave over a small-scale two-dimensional steep mountain is investigated in large-eddy simulations based on a fully compressible and nonhydrostatic model [Icosahedral Nonhydrostatic (ICON)] with triangular grids of 50-m-edge length. An idealized atmospheric profile derived from a realistic case is designed to account for influences from the stagnant layer near the surface, the stability of the atmospheric boundary layer (ABL) and the upper-level jet. First, simulations were done to bridge from the linear regime to the nonlinear regime by increasing the mountain height, which showed that larger-amplitude lee waves with longer wavelength can be produced in the nonlinear regime than in the linear regime. Second, the effects of the stagnant layer near the surface and the ABL stability were explored, which showed that the stagnant layer or the stable ABL can play a similar wave-absorbing role in the nonlinear regime as in linear theories or simulations. Third, the role of the upper-level jet was explored, indicating that a stronger (weaker) upper-level jet can help to produce longer (shorter) lee waves. The stable ABL with a stagnant layer can more (less) efficiently absorb the longer (shorter) lee waves due to the stronger (weaker) jet, so that the wave response is more sensitive to the wave-absorption layer when an upper-level jet is present. Finally, the momentum budget was analyzed to explore the interaction between the upper and lower levels of the troposphere, which showed that the momentum flux due to the upward-propagating waves and trapped waves varies with the upper-level jet strength and low-level stagnancy and ABL stability.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Haile Xue, xuehl@cma.gov.cn

Abstract

The diurnally evolving trapped lee wave over a small-scale two-dimensional steep mountain is investigated in large-eddy simulations based on a fully compressible and nonhydrostatic model [Icosahedral Nonhydrostatic (ICON)] with triangular grids of 50-m-edge length. An idealized atmospheric profile derived from a realistic case is designed to account for influences from the stagnant layer near the surface, the stability of the atmospheric boundary layer (ABL) and the upper-level jet. First, simulations were done to bridge from the linear regime to the nonlinear regime by increasing the mountain height, which showed that larger-amplitude lee waves with longer wavelength can be produced in the nonlinear regime than in the linear regime. Second, the effects of the stagnant layer near the surface and the ABL stability were explored, which showed that the stagnant layer or the stable ABL can play a similar wave-absorbing role in the nonlinear regime as in linear theories or simulations. Third, the role of the upper-level jet was explored, indicating that a stronger (weaker) upper-level jet can help to produce longer (shorter) lee waves. The stable ABL with a stagnant layer can more (less) efficiently absorb the longer (shorter) lee waves due to the stronger (weaker) jet, so that the wave response is more sensitive to the wave-absorption layer when an upper-level jet is present. Finally, the momentum budget was analyzed to explore the interaction between the upper and lower levels of the troposphere, which showed that the momentum flux due to the upward-propagating waves and trapped waves varies with the upper-level jet strength and low-level stagnancy and ABL stability.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Haile Xue, xuehl@cma.gov.cn
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