• Alaka, M. A., Ed., 1960: The airflow over mountains. WMO Tech. Note 34, 135 pp.

  • Black, T. M., 1994: The new NMC mesoscale Eta model: Description and forecast examples. Wea. Forecasting,9, 265–278.

  • Bretherton, F. P., 1969: Momentum transport by gravity waves. Quart. J. Roy. Meteor. Soc.,95, 213–243.

  • Bryan, K., 1969: A numerical method for the study of the circulation of the World Ocean. J. Comput. Phys.,4, 347–376.

  • Dudhia, J., 1993: A nonhydrostatic version of the Penn State–NCAR mesoscale model: Validation tests and simulation of an Atlantic cyclone and cold front. Mon. Wea. Rev.,121, 1493–1513.

  • Durran, D. R., and J. B. Klemp, 1983: A compressible model for the simulation of moist mountain waves. Mon. Wea. Rev.,111, 2341–2361.

  • Gal-Chen, T., and R. Somerville, 1975: On the use of coordinate a transformation for the solution of the Navier–Stokes equations. J. Comput. Phys.,17, 209–228.

  • Gallus, W. A., Jr., and M. Rancic, 1996: A nonhydrostatic version of the NMC’s regional eta model. Quart. J. Roy. Meteor. Soc.,122, 495–513.

  • Janjic, Z. I., 1984: Nonlinear advection schemes and energy cascade on semi-staggered grids. Mon. Wea. Rev.,112, 1234–1245.

  • ——, 1990: The step-mountain coordinate: Physical package. Mon. Wea. Rev.,118, 1429–1443.

  • ——, 1994: The step-mountain eta coordinate model: Further developments of the convection, viscous sublayer, and turbulence closure schemes. Mon. Wea. Rev.,122, 928–945.

  • Mesinger, F., 1984: A blocking technique for representation of mountains in atmospheric models. Riv. Meteor. Aeronaut.,44, 195–202.

  • ——, and Z. I. Janjic, 1985: Problems and numerical methods of incorporation of mountains in atmospheric models. Large-Scale Computations in Fluid Mechanics, Part 2, Lectures in Applied Mathematics, Vol. 22, Amer. Math. Soc., 81–120.

  • ——, ——, S. Nickovic, D. Gavrilov, and D. G. Deaven, 1988: The step mountain coordinate: Model description and performance for cases of alpine cyclogenesis and for a case of an Appalachian redevelopment. Mon. Wea. Rev.,116, 1493–1518.

  • Phillips, N. A., 1957: A coordinate system having some special advantages for numerical forecasting. J. Meteor.,14, 184–185.

  • Queney, P., 1948: The problem of air flow over mountains: A summary of theoretical studies. Bull. Amer. Meteor. Soc.,29, 16–26.

  • Rogers, E., and Coauthors, 1998: Changes to the NCEP operational“early” eta analysis/forecast system. NWS Tech. Procedures Bull. 447, National Oceanic and Atmospheric Administration/National Weather Service, 34 pp. [Available from National Weather Service, Office of Meteorology, 1325 East–West Highway, Silver Spring, MD 20910.].

  • Staudenmaier, M. J., and J. Mittelstadt, 1997: Results of the western region evaluation of the Eta-10 model. Western Region Tech. Attachment 97-18, 8 pp. [Available from National Weather Service Western Region-SSD, Rm. 1311, 125 S. State St., Salt Lake City, UT 84147; or online at http://nimbo.wrh.noaa.gov/wrhq/97TAs/TA9718/TA97-18.html.].

  • Takacs, L. L., 1985: A two-step scheme for the advection equation with minimized dissipation and dispersion errors. Mon. Wea. Rev.,113, 1050–1065.

  • Zhang, D.-L., and K. Gao, 1989: Numerical simulation of an intense squall line during 10–11 June 1985 PRE-STORM. Part II: Rear inflow, surface pressure perturbations and stratiform precipitation. Mon. Wea. Rev.,117, 2067–2094.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 2 2 2
PDF Downloads 3 3 3

Behavior of Flow over Step Orography

View More View Less
  • 1 Department of Geological and Atmospheric Sciences, Iowa State University, Ames, Iowa
  • | 2 National Center for Atmospheric Research, Boulder, Colorado
Restricted access

Abstract

A two-dimensional nonhydrostatic version of the NCEP regional Eta Model together with analytic theory are used to examine flow over isolated mountains in numerical simulations using a step-terrain vertical coordinate. Linear theory indicates that a singularity arises in the steady flow over the step corners for hydrostatic waves and that this discontinuity is independent of height. Analytic solutions for both hydrostatic and nonhydrostatic waves reveal a complex behavior that varies with both horizontal and vertical resolution.

Witch of Agnessi experiments are performed with a 2D version of the Eta Model over a range of mountain half-widths. The simulations reveal that for inviscid flow over a mountain using the step-terrain coordinate, flow will not properly descend along the lee slope. Rather, the flow separates downstream of the mountain and creates a zone of artificially weak flow along the lee slope. This behavior arises due to artificial vorticity production at the corner of each step and can be remedied by altering the finite differencing adjacent to the step to minimize spurious vorticity production.

In numerical simulations with the step-terrain coordinate for narrow mountains where nonhydrostatic effects are important, the disturbances that arise at step corners may be of the same horizontal scale as those produced by the overall mountain, and the superposition of these disturbances may reasonably approximate the structure of the continuous mountain wave. For wider mountains, where perturbations are nearly hydrostatic, the disturbances above the step corners have horizontal scales that are much smaller than the overall scale of the mountain and appear as sharp spikes in the flow field. The deviations from the “classic” Witch of Agnesi solution are significant unless the vertical resolution is very small compared to the height of the mountain. In contrast, simulations with the terrain-following vertical coordinate produce accurate solutions provided the vertical grid interval is small compared to the vertical wavelength of the mountain waves (typically at least an order of magnitude larger than the mountain height).

Corresponding author address: Dr. William A. Gallus Jr., Department of Geological and Atmospheric Sciences, Iowa State University, 3025 Agronomy Hall, Ames, IA 50011.

Email: wgallus@iastate.edu

Abstract

A two-dimensional nonhydrostatic version of the NCEP regional Eta Model together with analytic theory are used to examine flow over isolated mountains in numerical simulations using a step-terrain vertical coordinate. Linear theory indicates that a singularity arises in the steady flow over the step corners for hydrostatic waves and that this discontinuity is independent of height. Analytic solutions for both hydrostatic and nonhydrostatic waves reveal a complex behavior that varies with both horizontal and vertical resolution.

Witch of Agnessi experiments are performed with a 2D version of the Eta Model over a range of mountain half-widths. The simulations reveal that for inviscid flow over a mountain using the step-terrain coordinate, flow will not properly descend along the lee slope. Rather, the flow separates downstream of the mountain and creates a zone of artificially weak flow along the lee slope. This behavior arises due to artificial vorticity production at the corner of each step and can be remedied by altering the finite differencing adjacent to the step to minimize spurious vorticity production.

In numerical simulations with the step-terrain coordinate for narrow mountains where nonhydrostatic effects are important, the disturbances that arise at step corners may be of the same horizontal scale as those produced by the overall mountain, and the superposition of these disturbances may reasonably approximate the structure of the continuous mountain wave. For wider mountains, where perturbations are nearly hydrostatic, the disturbances above the step corners have horizontal scales that are much smaller than the overall scale of the mountain and appear as sharp spikes in the flow field. The deviations from the “classic” Witch of Agnesi solution are significant unless the vertical resolution is very small compared to the height of the mountain. In contrast, simulations with the terrain-following vertical coordinate produce accurate solutions provided the vertical grid interval is small compared to the vertical wavelength of the mountain waves (typically at least an order of magnitude larger than the mountain height).

Corresponding author address: Dr. William A. Gallus Jr., Department of Geological and Atmospheric Sciences, Iowa State University, 3025 Agronomy Hall, Ames, IA 50011.

Email: wgallus@iastate.edu

Save