Two-Layer Stratified Flow past a Valley

Richard Rotunno National Center for Atmospheric Research, Boulder, Colorado

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Manuela Lehner Department of Atmospheric Sciences, University of Utah, Salt Lake City, Utah

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Abstract

Observations and models of nocturnal katabatic winds indicate strong low-level stability with much weaker stability aloft. When such winds encounter an embedded depression in an otherwise smooth sloping plane, the flow responds in a manner that is largely describable by the inviscid fluid dynamics of stratified flow. Building on earlier work, the present study presents a series of numerical simulations based on the simplest nontrivial idealization relevant to the observations: the height-independent flow of a two-layer stratified fluid past a two-dimensional valley. Stratified flow past a valley has received much less attention than the related problem of stratified flow past a hill. Hence, the present paper gives a detailed review of existing theory and fills a few gaps along the way. The theory is used as an interpretive guide to an extensive set of numerical simulations. The solutions exhibit a variety of behaviors that depend on the nondimensional input parameters. These behaviors range from complete flow through the valley to valley-flow stagnation to situations involving internal wave breaking, lee waves, and quasi-stationary waves in the valley. A diagram is presented that organizes the solutions into flow regimes as a function of the nondimensional input parameters.

Corresponding author address: Richard Rotunno, National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO 80307. E-mail: rotunno@ucar.edu

Abstract

Observations and models of nocturnal katabatic winds indicate strong low-level stability with much weaker stability aloft. When such winds encounter an embedded depression in an otherwise smooth sloping plane, the flow responds in a manner that is largely describable by the inviscid fluid dynamics of stratified flow. Building on earlier work, the present study presents a series of numerical simulations based on the simplest nontrivial idealization relevant to the observations: the height-independent flow of a two-layer stratified fluid past a two-dimensional valley. Stratified flow past a valley has received much less attention than the related problem of stratified flow past a hill. Hence, the present paper gives a detailed review of existing theory and fills a few gaps along the way. The theory is used as an interpretive guide to an extensive set of numerical simulations. The solutions exhibit a variety of behaviors that depend on the nondimensional input parameters. These behaviors range from complete flow through the valley to valley-flow stagnation to situations involving internal wave breaking, lee waves, and quasi-stationary waves in the valley. A diagram is presented that organizes the solutions into flow regimes as a function of the nondimensional input parameters.

Corresponding author address: Richard Rotunno, National Center for Atmospheric Research, P. O. Box 3000, Boulder, CO 80307. E-mail: rotunno@ucar.edu
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  • Baines, P. G., 1995: Topographic Effects in Stratified Flow. Cambridge University Press, 482 pp.

  • Baines, P. G., and H. Granek, 1990: Hydraulic models of deep stratified flows over topography. The Physical Oceanography of Sea Straights, L. J. Pratt, Ed., NATO ASI Series, Vol. 318, Kluwer, 245–269, doi:10.1007/978-94-009-0677-8_12.

  • Benjamin, T. B., and M. Lighthill, 1954: On cnoidal waves and bores. Proc. Roy. Soc. London, 224A, 448460, doi:10.1098/rspa.1954.0172.

    • Search Google Scholar
    • Export Citation
  • Bryan, G. H., and J. M. Fritsch, 2002: A benchmark simulation for moist nonhydrostatic numerical models. Mon. Wea. Rev., 130, 29172928, doi:10.1175/1520-0493(2002)130<2917:ABSFMN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Durran, D. R., and J. B. Klemp, 1987: Another look at downslope winds. Part II: Nonlinear amplification beneath wave-overturning layers. J. Atmos. Sci., 44, 34023412, doi:10.1175/1520-0469(1987)044<3402:ALADWP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Kimura, F., and P. Manins, 1988: Blocking in periodic valleys. Bound.-Layer Meteor., 44, 137169, doi:10.1007/BF00117296.

  • Lehner, M., and Coauthors, 2016a: The METCRAX II field experiment: A study of downslope windstorm-type flows in Arizona’s Meteor Crater. Bull. Amer. Meteor. Soc., 97, 215235, doi:10.1175/BAMS-D-14-00238.1.

    • Search Google Scholar
    • Export Citation
  • Lehner, M., R. Rotunno, and C. D. Whiteman, 2016b: Flow regimes over a basin induced by upstream katabatic flows—An idealized modeling study. J. Atmos. Sci., 73, 38213842, doi:10.1175/JAS-D-16-0114.1.

    • Search Google Scholar
    • Export Citation
  • Long, R. R., 1953: Some aspects of the flow of stratified fluids. I. A theoretical investigation. Tellus, 5A, 4258, doi:10.1111/j.2153-3490.1953.tb01035.x.

    • Search Google Scholar
    • Export Citation
  • Ogura, Y., and N. A. Phillips, 1962: Scale analysis of deep and shallow convection in the atmosphere. J. Atmos. Sci., 19, 173179, doi:10.1175/1520-0469(1962)019<0173:SAODAS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Rayleigh, L., 1914: On the theory of long waves and bores. Proc. Roy. Soc. London, 90A, 324328, doi:10.1098/rspa.1914.0055.

  • Smith, R. B., 1985: On severe downslope windstorms. J. Atmos. Sci., 42, 25972603, doi:10.1175/1520-0469(1985)042<2597:OSDW>2.0.CO;2.

  • Yih, C.-S., 1965: Dynamics of Nonhomogeneous Fluids. Macmillan, 306 pp.

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