Abstract
The onset of separation in turbulent, neutrally stratified, boundary-layer flow over hills is considered. Since the flows are fully turbulent, the occurrence of intermittent separation, in the sense of any reversal of near surface flow, will depend strongly on the detailed structure and behaviour of the turbulent eddies. Very little is known about such intermittent separation and the phenomenon cannot be studied with numerical models employing standard turbulence closures; eddy-resolving models are required. Therefore, here, as elsewhere in the literature, the arguably less physically significant process of mean flow separation is studied. Numerical simulations of flow over idealised two- and three-dimensional hills are examined in detail to determine the lowest slope,Θ crit, for which the mean flow separates.
Previous work has identified this critical slope as that required to produce a zero surface stress somewhere over the hill. This criterion, when a mixing-length turbulence closure is applied, reduces to requiring the near-surface vertical velocity shear to vanish at some point on the hill's surface. By applying results from a recent linear analysis for the flow perturbations to this condition, a new expression forΘ crit is obtained. The expression is approximate but its relative simplicity makes it practically applicable without the need for use of a computer or for detailed mapping of the hill. The approach suggested differs from previous ones in that it applies linear results to a non-linear expression for the surface stress. In the past, a linear expression for the surface stress has been used. The proposed expression forΘ crit leads to critical angles that are about twice previous predictions. It is shown that the present expression gives good agreement with the numerical results presented here, as well as with other numerical and experimental results. It is also consistent with atmospheric observations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Belcher, S. E.: 1990,Turbulent Boundary Layer Flow over Undulating Surfaces, Ph.D. dissertation, Cambridge University.
Belcher, S. E., Newley, T. M. J., and Hunt, J. C. R.: 1993, ‘The Drag on an Undulating Surface Due to the Flow of a Turbulent Boundary Layer’,J. Fluid Mech. 249, 557–596.
BRE: 1989,The Assessment of Wind Speed over Topography, Building Research Establishment, Digest 346, HMSO, London.
Britter, R. E., Hunt, J. C. R., and Richards K. J.: 1981, ‘Air Flow over a Two-Dimensional Hill: Studies of Velocity Speed-Up, Roughness Effects and Turbulence’,Quart. J. Roy. Meteorol. Soc. 107, 91–110.
Clark, T. L.: 1977. ‘A Small-Scale Dynamic Model using a Terrain-Following Transformation’,J. Comput. Phys. 24, 186–215.
Giostra, U., Tampieri, F. and Trombetti, F 1989, ‘On the Onset of Separation in Turbulent Boundary Layer Flow over Two-Dimensional Humps of Various Size’,Nuovo Cimento,12C, 649–661.
Grant, A. L. M. and Mason, P. J.: 1990, ‘Observations of Boundary-Layer Structure over Complex Terrain’,Quart. J. Roy. Meteorol. Soc. 116, 159–186.
Gong, W. and Ibbetson, A.: 1989, ‘A Wind Tunnel Study of Turbulent Flow over Model Hills’,Boundary-Layer Meteorol 49, 113–148.
Hunt, J. C. R., Abell, C. J., Peterka, J. A., and Woo, H. 1978, ‘Kinematical Studies of Flow Around Free or Surface-Mounted Obstacles; Applying Topology to Flow Visualisation’,J. Fluid Mech. 86, 179–200.
Hunt, J. C. R., Leibovich, S., and Richards, K. J.: 1988, ‘Turbulent Shear Flows over Low Hills’,Quart. J. Roy. Meteorol. Soc. 114, 1435–1470.
Hunt, J. C. R. and Simpson, J. E.: 1982, ‘Atmospheric Boundary Layers over Non-Homogeneous Terrain’, in E. J. Plate (ed.),Engineering Meteorology, Chapter 7, Elsevier Sci., Amsterdam, pp. 269–318.
Jackson, P. S. and Hunt, J. C. R.: 1975, ‘Turbulent Wind Flow over a Low Hill’,Quart. J. Roy. Meteorol. Soc. 101, 929–955.
Lighthill, J.: 1989,An Informal Introduction to Theoretical Fluid Mechanics, Oxford, Clarendon Press, 260 pp.
Mason, P. J.: 1986, ‘Flow over the Summit of an Isolated Hill’,Boundary-Layer Meteorol.37, 385–405.
Mason, P. J. and King, J. C.: 1984, ‘Atmospheric Flow over a Succession of Nearly Two-Dimensional Ridges and Valleys’,Quart. J. Roy. Meteorol. Soc. 110, 821–845.
Mason, P. J. and King, J. C.: 1985, ‘Measurements and Predictions of Flow and Turbulence over an Isolated Hill of Moderate Slope’,Quart. J. Roy. Meteorol. Soc. 111, 617–640.
Mason, P. J. and Sykes, R. I.: 1979a, ‘Three-Dimensional Numerical Integrations of the Navier-Stokes Equations for Flow over Surface-Mounted Obstacles’,J. Fluid Mech. 91, 433–450.
Mason, P. J. and Sykes, R. I.: 1979b, ‘Separation Effects in Ekman Layer Flow over Ridges’,Quart. J. Roy. Meteorol. Soc. 105, 129–146.
Mason, P. J. and Sykes, R. I.: 1979c, ‘Flow over an Isolated Hill of Moderate Slope’,Quart. J. Roy. Meteorol. Soc. 105, 383–395.
Nanni, S. C. and Tampieri, F.: 1985, ‘A Linear Investigation on Separation in Laminar and Turbulent Boundary Layers over Low Hills and Valleys’,Nuovo Cimento 8C 579–601.
Newley, T. J.: 1985,Turbulent Airflow over Hills, Ph.D. dissertation, Cambridge University.
Salmon, J. R., Bowen, A. J., Hoff, A. M., Johnson, R., Mickle, R. E., Taylor, P. A., Tetzlaff, G., and Walmsley, J. L.: 1988a, ‘The Askervein Hill Project: Mean Wind Variations at Fixed Heights Above Ground’,Boundary-Layer Meteorol. 43, 247–271.
Salmon, J. R., Teunissen, H. W., Mickle, R. E., and Taylor, P. A.: 1988b, ‘The Kettles Hill Project: Field Observations, Wind-Tunnel Simulations and Numerical Model Predictions for Flow over a Low Hill’,Boundary-Layer Meteorol. 43, 309–343.
Tampieri, F.: 1987, ‘Separation Features of Boundary-Layer Flow over Valleys’,Boundary-Layer Meteorol. 40, 295–307.
Taylor, P. A., Gent, P. R., and Keen, J. M.: 1976, ‘Some Numerical Solutions for Turbulent Boundary Layer Flow above Fixed, Rough, Wavy Surfaces’,Geophys. J. R. Astr. Soc. 44, 177–201.
Taylor, P. A. and Lee, R. J.: 1984, ‘Simple Guidelines for Estimating Wind Speed Variations due to Small Scale Topographic Features’,Climatol. Bulletin 18, 3–32.
Taylor, P. A. and Teunissen, H. W.: 1987, ‘The Askervein Hill Project: Overview and Background Data’,Boundary-Layer Meteorol. 39, 15–39.
Teunissen, H. W., Shokr, M. E., Bowen, A. J. Wood, C. J., and Green, D. W. R.: 1987, ‘The Askervein Hill Project: Wind-Tunnel Simulations at Three Length Scales’,Boundary-Layer Meteorol. 40, 1–29.
Van Dommelen, L. L. and Cowley, S. J.: 1990, ‘On the Lagrangian Description of Unsteady Boundary-Layer Separation. Part 1. General Theory’,J. Fluid Mech. 210, 593–626.
Wood, N.: 1992,Turbulent Flow over Three-Dimensional Hills Ph.D. thesis. University of Reading.
Wood, N. and Mason, P. J.: 1993, ‘The Pressure Force Induced by Neutral Turbulent Flow over Hills’,Quart. J. Roy. Meteorol. Soc. 119, 1233–1267.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wood, N. The onset of separation in neutral, turbulent flow over hills. Boundary-Layer Meteorol 76, 137–164 (1995). https://doi.org/10.1007/BF00710894
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00710894