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Turbulent boundary-layer flow over fixed aerodynamically rough two-dimensional sinusoidal waves

Published online by Cambridge University Press:  26 April 2006

W. Gong
Affiliation:
ARQI, Atmospheric Environment Service, 4905, Dufferin St., Downsview, Ontario, Canada, M3H 5T4
Peter A. Taylor
Affiliation:
Department of Earth and Atmospheric Science, York University, North York, Ontario, Canada, M3J 1P3
Andreas Dörnbrack
Affiliation:
Institute of Atmospheric Physics, DLR, D-82230, Oberpfaffenhofen, Germany

Abstract

Results from a wind tunnel study of aerodynamically rough turbulent boundary-layer flow over a sinusoidal surface are presented. The waves had a maximum slope (ak) of 0.5 and two surface roughnesses were used. For the relatively rough surface the flow separated in the wave troughs while for the relatively smooth surface it generally remained attached. Over the relatively smooth-surfaced waves an organized secondary flow developed, consisting of vortex pairs of a scale comparable to the boundary-layer depth and aligned with the mean flow. Large-eddy simulation studies model the flows well and provide supporting evidence for the existence of this secondary flow.

Type
Research Article
Copyright
© 1996 Cambridge University Press

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References

Abrahams, J. & Hanratty, T. J. 1985 Relaxation effects over a wavy surface. J. Fluid Mech. 151, 443455.Google Scholar
Ayotte, K. W., Xu, D. & Taylor, P. A. 1994 The impact of different turbulent closures on predictions of the mixed spectral finite difference model for flow over topography. Boundary-Layer Met. 68, 133.Google Scholar
Bandou, T. & Mitsuyasu, H. 1988 The structure of turbulent air flow over a wavy wall, Part 2, Rep. Res. Inst. for Appl. Mech. Kyushu University, No 104, 1334.
Beebe, P. S. & Cermak, J. E. 1972 Turbulent flow over a wavy boundary. Tech. Rep. 16, CER 7172 PSB-JEC 44, Fluid Dynamics and Diffusion Laboratory, Colorado State University, Fort Collins, Colorado, USA.
Beljaars, A. C. M., Walmsley, J. L. & Taylor, P. A. 1987 A mixed spectral finite difference model for neutrally stratified boundary-layer flow over roughness change and topography. Boundary-Layer Met. 38, 273303.Google Scholar
Britter, R. E., Hunt, J. C. R. & Richards, K. J. 1981 Airflow over a two dimensional hill; studies of velocity speed-up, roughness effects and turbulence. Q. J. R. Met. Soc. 107, 91110.Google Scholar
Buckles, J., Hanratty, T. J. & Adrian, R. J. 1984 Turbulent flow over large-amplitude wavy surfaces. J. Fluid Mech. 140, 2744.Google Scholar
Caponi, E. A., Fornberg, B., Knight, D. D., McLean, J. W., Saffman, P. G. & Yuen, H. C. 1982 Calculations of laminar viscous flow over a moving wavy surface. J. Fluid Mech. 124, 347362.Google Scholar
Carruthers, D. J. & Hunt, J. C. R. 1990 Fluid mechanics of airflow over hills: turbulence, fluxes and waves in the boundary layer. In Atmospheric Processes over Complex Terrain (ed.W. Blumen). AMS Meteorological Monographs, 23, no 45, pp. 83107.
Counihan, J. 1974 Flow over concatenated sinusoidal hills. Central Elect. Res. Lab., UK. Rep. RD/L/N57/74.
Counihan, J. 1975 Adiabatic atmospheric boundary layers: a review and analysis of data from the period 1880–1972, 1880 –1972. Atmos. Environ. 9, 871905.Google Scholar
Craik, A. D. D. 1982 Wave-induced longitudinal-vortex instability in shear flows. J. Fluid Mech. 125, 3572.Google Scholar
Dörnbrack, A. & Schumann, U. 1993 Numerical simulation of turbulent convective flow over wavy terrain. Boundary-Layer Met. 65, 323355.Google Scholar
Finnigan, J. J. 1988 Air flow over complex terrain. In Flow and Transport in the Natural Environment (ed.W. L. Steffen & O. T. Denmead), pp. 183229. Springer.
Finnigan, J. J., Raupach, M. R., Bradley, E. F. & Alois, G. K. 1990 A wind tunnel study of turbulent flow over a two-dimensional ridge. Boundary-Layer Met. 50, 277317.Google Scholar
Garratt, J. R. 1992 The Atmospheric Boundary Layer. Cambridge University Press.
Gent, P. R. & Taylor, P. A. 1977 A note on ‘separation’ over short wind waves. Boundary-Layer Met. 11, 6587.Google Scholar
Gong, W. & Ibbetson, A. 1989 A wind tunnel study of turbulent flow over model hills. Boundary-Layer Met. 49, 113148.Google Scholar
Görtler, H. 1940 Uber eine dreidimensionale Instabilitaet laminarer Grenzschichten an konkaven Waenden. Nachr. Ges. Wiss. Goettingen, Math.-Phys. Klasse, Neue Folge I, 2, 126.
Hoffmann, P. H., Muck, K. C. & Bradshaw, P. 1985 The effect of concave surface curvature on turbulent boundary layers. J. Fluid Mech. 161, 371403.Google Scholar
Hsu, S.-T. & Kennedy, J. F. 1971 Turbulent flow in wavy pipes. J. Fluid Mech. 47, 481502.Google Scholar
Hunt, J. C. R., Tampieri, F., Weng, W. S. & Carruthers, D. J. 1991 Air flow and turbulence over complex terrain: a colloquium and a computational workshop. J. Fluid Mech. 227, 667688.Google Scholar
Jackson, P. S. & Hunt, J. C. R. 1975 Turbulent wind flow over a low hill. Q. J. R. Met. Soc. 101, 929955.Google Scholar
Kaimal, J. C. & Finnigan, J. J. 1994 Atmospheric Boundary Layer Flows: their Structure and Measurement. Oxford University Press.
Kendall, J. M. 1970 The turbulent boundary layer over a wall with progressive surface waves. J. Fluid Mech. 41, 259281.Google Scholar
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Rep. 1247.
Krettenauer, K. & Schumann, U. 1992 Numerical simulation of turbulent convection over wavy terrain. J. Fluid Mech. 237, 261299.Google Scholar
Kuzan, J. D., Hanratty, T. J. & Adrian, R. J. 1989 Turbulent flows with incipient separation over solid waves. Exps. Fluids 7, 8898.Google Scholar
Lasheras, J. C., Cho, J. S. & Maxworthy, T. 1986 On the origin and evolution of streamwise vortical structure in a plane, free shear layer. J. Fluid Mech. 172, 231258.Google Scholar
Lawson, R. E. & Britter, R. E. 1983 A note on the measurement of transverse velocity fluctuations with heated cylindrical sensors at small mean velocities. J. Phys. E: Sci. Instrum. 16, 563567.Google Scholar
Maas, C. & Schumann, U. 1994 Numerical simulation of turbulent flow over a wavy boundary. In Direct and Large Eddy Simulation I (ed . P. R. Voke, L. Kleiser & J. P. Chollet), pp. 287297. Kluwer.
Maat, N. & Makin, V. K. 1992 Numerical simulation of air flow over breaking waves. Boundary-Layer Met. 60, 7793.Google Scholar
Mason, P. J. 1994 Large-eddy simulation: a critical review of the technique. Q. J. R. Met. Soc. 120, 126.Google Scholar
Mickle, R. E., Cook, N. J., Hoff, A. M., Jensen, N. O., Salmon, J. R., Taylor, P. Atetzlaff, G. & Teunissen, H. W. 1988 The Askervein hill project: vertical profiles of wind and turbulence. Boundary-Layer Met. 43, 143169.Google Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185204.Google Scholar
Motzfeld, H. 1937 Die turbulente Strömung an welligen Wanden. Z. Angew. Math. Mech. 17, 193212.Google Scholar
Newley, T. M. J. 1985 Turbulent airflow over hills. PhD thesis, University of Cambridge, UK.
Panofsky, H. A. & Dutton, J. A. 1983 Atmospheric Turbulence: Models and Methods for Engineering Applications. Wiley.
Phillips, W. R. C. & Wu, Z. 1994 On the instability of wave-catalysed longitudinal vortices in strong shear. J. Fluid Mech. 272, 235254.Google Scholar
Shokr, M. & Teunissen, H. W. 1988 Use of hot-wire anemometry in the AES boundary-layer wind tunnel with particular reference to flow over hill models. Res. Rep. MSRB 889. AES, 4905 Dufferin Street, Downsview, Ontario, Canada.
Stanton, T., Marshall, D. & Houghton, R. 1932 The growth of waves on water due to the action of the wind. Proc. R. Soc. Lond. A 137, 283293.Google Scholar
Stull, R. B. 1988 An Introduction to Boundary-Layer Meteorology. Kluwer.
Sutton, O. G. 1953 Micrometeorology. McGraw Hill.
Swearingen, J. D. & Blackwelder, R. F. 1986 Spacing of streamwise vortices on concave walls. AIAA J. 24, 17061709.Google Scholar
Taylor, P. A. 1977a Some numerical studies of surface boundary-layer flow above gentle topography. Boundary-Layer Met. 11, 439465.Google Scholar
Taylor, P. A. 1977b Numerical studies of neutrally stratified planetary boundary-layer flow above gentle topography 1. Two-dimensional cases. Boundary-Layer Met. 12, 3760.Google Scholar
Taylor, P. A., Mason, P. J. & Bradley, E. F. 1987 Boundary-layer flow over low hills – A review. Boundary-Layer Met. 39, 107132.Google Scholar
Taylor, P. A., Sykes, R. I. & Mason, P. J. 1989 On the parameterisation of drag over small-scale topography in neutrally-stratified boundary-layer flow. Boundary-Layer Met. 48, 409422.Google Scholar
Taylor, P. A., Xu, D., Gong, W. & Ayotte, K. W. 1995 Modelling turbulent boundary-layer flow over 2D sinusoidal waves. Proc. Intl Symp. on the Air-Sea Interface. University of Toronto Press (to appear).
Teunissen, H. W. & Flay, R. G. J. 1981 Wind-tunnel simulation of planetary boundary-layer flow over an isolated hill: Part 1, rough model. Rep. MSRB 813. AES, 4905 Dufferin Street, Downsview, Ontario, Canada.
Townsend, A. A. 1972 Flow in a deep turbulent boundary-layer over a surface distorted by water waves. J. Fluid Mech. 55, 719735.Google Scholar
Walmsley, J. L., Salmon, J. R. & Taylor, P. A. 1982 On the application of a model of boundary-layer flow over low hills to real terrain. Boundary-Layer Met. 23, 1746.Google Scholar
Wood, N. & Mason, P. J. 1993 The pressure force induced by neutral, turbulent flow over hills. Q. J. R. Met. Soc. 119, 12331267.Google Scholar
Xu, D., Ayotte, K. W. & Taylor, P. A. 1994 Development of the NLMSFD model of turbulent boundary-layer flow over topography. Boundary-Layer Met. 70, 341367.Google Scholar
Xu, D. & Taylor, P. A. 1992 A non-linear extension of the mixed spectral finite difference model for neutrally stratified flow over topography. Boundary-Layer Met. 59, 177186.Google Scholar
Zilker, D. P., Cook, G. W. & Hanratty, T. J. 1977 Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 1. Non-separated flows. J. Fluid Mech. 82, 2951.Google Scholar
Zilker, D. P. & Hanratty, T. J. 1979 Influence of the amplitude of a solid wavy wall on a turbulent flow. Part 2. Separated flows. J. Fluid Mech. 90, 257271.Google Scholar