Abstract
By means of a large-eddy simulation, the convective boundary layer is investigated for flows over wavy terrain. The lower surface varies sinusoidally in the downstream direction while remaining constant in the other. Several cases are considered with amplitude δ up to 0.15H and wavelength λ ofH to 8H, whereH is the mean fluid-layer height. At the lower surface, the vertical heat flux is prescribed to be constant and the momentum flux is determined locally from the Monin-Obukhov relationship with a roughness lengthz o=10−4 H. The mean wind is varied between zero and 5w *, wherew * is the convective velocity scale. After rather long times, the flow structure shows horizontal scales up to 4H, with a pattern similar to that over flat surfaces at corresponding shear friction. Weak mean wind destroys regular spatial structures induced by the surface undulation at zero mean wind. The surface heating suppresses mean-flow recirculation-regions even for steep surface waves. Short surface waves cause strong drag due to hydrostatic and dynamic pressure forces in addition to frictional drag. The pressure drag increases slowly with the mean velocity, and strongly with δ/H. The turbulence variances increase mainly in the lower half of the mixed layer forU/w *>2.
Similar content being viewed by others
References
Brutsaert, W. and Kustas, W. P.: 1987, ‘Surface Water Vapor and Momentum Fluxes under Unstable Conditions from a Rugged-Complex Area’,J. Atmos. Sci. 44, 421–431.
Brutsaert, W. and Sugita, M.: 1990, ‘The Extent of the Unstable Monin-Obukhov Layer for Temperature and Humidity above Complex Hilly Grassland’,Boundary-Layer Meteorol. 51, 383–400.
Buckles, J., Hanratty, T. J., and Adrian, R. J.: 1984, ‘Turbulent Flow over Large-Amplitude Wavy Surfaces’,J. Fluid Mech. 140, 27–44.
Druilhet, A., Noilhan, J., Benech, B., Dubosclard, G., Guedalia, D., and Frangi, J.: 1983, ‘Étude expérimentale de la couche limite au-dessus d'un relief modérè proche d'une chaîne de montagne’,Boundary-Layer Meteorol. 25, 3–16.
Emeis, S.: 1990, ‘Pressure Drag of Obstacles in the Atmospheric Boundary Layer’,J. Appl. Meteorol. 29, 461–476.
Grant, A. L. M. and Mason, P. J.: 1990, ‘Observations of Boundary-Layer Structure over Complex Terrain’,Quart. J. R. Meteorol. Soc. 116, 159–186.
Hadfield, M. G., Cotton, W. R., and Pielke, R. A.: 1991, ‘Large-Eddy Simulations of Thermally Forced Circulations in the Convective Boundary Layer. Part I. A Small-Scale Circulation with Zero Wind’,Boundary-Layer Meteorol. 57, 79–114.
Hadfield, M. G., Cotton, W. R., and Pielke, R. A.: 1992, ‘Large-Eddy Simulations of Thermally Forced Circulations in the Convective Boundary Layer. Part II. The Effect of Changes in Wavelength and Wind Speed’,Boundary-Layer Meteorol. 58, 307–327.
Hechtel, L. M., Moeng, C.-H., and Stull, R. B.: 1990, ‘The Effects of Nonhomogeneous Surface Fluxes on the Convective Boundary Layer: A Case Study Using Large-Eddy Simulation’,J. Atmos. Sci. 47, 1721–1741.
Hunt, J. C. R., Leibovich, S., and Richards, K. J.: 1988, ‘Turbulent Shear Flows over Low Hills’,Quart. J. R. Meteorol. Soc. 114, 1435–1470.
Hunt, J. C. R., Tampieri, F., Weng, W. S., and Carruthers, D. J.: 1991, ‘Air Flow and Turbulence over Complex Terrian: a Colloquium and a Computational Workshop’,J. Fluid Mech. 227, 667–688.
Huynh, B. P., Coulman, C. E., and Turner, T. R.: 1990, ‘Some Turbulence Characteristics of Convectively Mixed Layers over Rugged and Homogeneous Terrian’,Boundary-Layer Meteorol. 51, 229–254.
Kaimal, J. C., Eversole, R. A., Lenschow, D. H., Stankow, B. B., Kahn P. H., and Businger, J. A.: 1982, ‘Spectral Characteristics of the Convective Boundary Layer over Unevell Terrain’,J. Atmos. Sci. 39, 1098–1114.
Krettenauer, K., and Schumann, U.: 1989, ‘Direct Numerical Simulation of Thermal Convection over a Wavy Surface’,Meteorol. Atmos. Phys. 41, 165–179.
Krettenauer, K., and Schumann, U.: 1992, ‘Numerical Simulation of Turbulent Convection over Wavy Terrain’,J. Fluid Mech. 237, 261–299.
Krishnamurti, R., and Howard, L. N.: 1981, ‘Large-scale Flow Generation in Turbulent Convection’,Proc. Natl. Acad. Sci. USA 78, 1981–1985.
Mason, P. J.: 1987, ‘Diurnal Variations in Flow over a Succession of Ridges and Valleys’,Quart. J. R. Meteorol. Soc. 113, 117–1140.
Mason, P. J., and King, J. C.: 1984, ‘Atmospheric Flow over a Succession of Nearly Two-Dimensional Ridges and Valleys’,Quart. J. R. Meteorol. Soc. 110, 821–845.
Nieuwstadt, F. T. M., Mason, P. J., Moeng, C.-H., and Schumann., U.: 1992, ‘Large-Eddy Simulation of the Convective Boundary Layer: A Comparison of Four Computer Codes’, in F. Furstet al. (eds.),Turbulent Shear Flows 8, Springer, 343–368.
Raasch, S., and Groß, G.: 1992, ‘VISES: Visualisierung numerischer Simulationsergebnisse mittels Videofilm’,Meteorol. Z.,1, 211.
Raupach, M. R., Weng, W. S., Carruthers, and Hunt, J. C. R.: 1992, ‘Temperature and Humidity Fields and Fluxes over Low Hills’,Quart. J. R Meteorol. Soc. 118, 191–225.
Schmidt, H., and Schumann, U.: 1989, ‘Coherent Structure of the Convective Boundary Layer Deduced from Large-Eddy Simulation’,J. Fluid Mech. 200, 511–562.
Schumann, U.: 1988, ‘Minimum Friction Velocity and Heat Transfer in the Rough Surface Layer of a Convective Boundary Layer’,Boundary-Layer Meteorol. 44, 311–326.
Schumann, U.: 1990, ‘Large-Eddy Simulation of the Up-Slope Boundary Layer’,Quart. J. R. Meteorol. Soc. 116, 637–670.
Schumann, U.: 1991a, ‘Subgrid Length-Scales for Large-Eddy Simulation of Stratified Turbulence’,Theor. Comput. Fluid Dyn. 2, 279–290.
Schumann, U.: 1991b, ‘A Simple Model of the Convective Boundary Layer over Wavy Terrain with Variable Heat Flux’,Beitr. Phys. Atmosph. 64, 169–184.
Schumann, U.: 1993, ‘Transport Asymmetry in Skewed Convective Circulations’,J. Atmos. Sci. 50, 116–119.
Scorer, R. S.: 1978,Environmental Aerodynamics, J. Wiley.
Sykes, R. I. and Henn, D. S.: 1989, ‘Large-Eddy, Simulation of Turbulent Sheared Convection’,J. Atmos. Sci. 46, 1106–1118.
Tampieri, F.: 1987, ‘Separation Features of Boundary-Layer Flow over Valleys’,Boundary-Layer Meteorol. 40, 295–307.
Taylor, P. A.: 1977, ‘Some Numerical Studies of Surface Boundary-Layer Flow above Gentle Topography’,Boundary-Layer Meteorol. 11, 439–465.
Taylor P. A., Mason, P. J., and Bradley, E. F.: 1987, ‘Boundary-Layer Flow over Low Hills’,Boundary-Layer Meteorol. 39, 107–132.
Taylor, P. A., Sykes, R. I., and Mason, P. J.: 1989, ‘On the Parameterization of Drag over Small-Scale Topography in Neutrally-Stratified Boundary-Layer Flow’,Boundary-Layer Meteorol. 48, 409–422.
Walko, R. L., Cotton, W. R., and Pielke, R. A.: 1992, ‘Large-Eddy Simulations of the Effects of Hilly Terrain on the Convective Boundary Layer’,Boundary-Layer Meteorol. 58, 133–150.
Zeman, O. and Jensen, N. O.: 1987, ‘Modification of Turbulence Characteristics in Flow over Hills’,Quart. J. R. Meteorol. Soc. 113, 55–80.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dörnbrack, A., Schumann, U. Numerical simulation of turbulent convective flow over wavy terrain. Boundary-Layer Meteorol 65, 323–355 (1993). https://doi.org/10.1007/BF00707032
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00707032