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A numerical study of the turbulent Ekman layer

Published online by Cambridge University Press:  26 April 2006

G. N. Coleman ,
J. H. Ferziger  and
P. R. Spalart
G. N. Coleman
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford CA 94305, USA
J. H. Ferziger
Affiliation:
NASA Ames Research Center, Moffett Field CA 94035, USA
P. R. Spalart
Affiliation:
NASA Ames Research Center, Moffett Field CA 94035, USA
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Abstract

The three-dimensional time-dependent turbulent flow in a neutrally stratified Ekman layer over a smooth surface is computed numerically by directly solving the Navier–Stokes equations. All the relevant scales of motion are included in the simulation so that no turbulence model is needed. Results of the simulations indicate that the horizontal component of the rotation vector has a significant influence on the turbulence; thus the ‘f-plane’ approximation fails. Differences as large as 20% in the geostrophic drag coefficient, u*/G, and 70% in the angle between the freestream velocity and the surface shear stress are found, depending on the latitude and the direction of the geostrophic wind. At 45° latitude, differences of 6 and 30% are noted in the drag coefficient and the shear angle, respectively, owing to the variation of the wind direction alone. Asymptotic similarity theory and a higher-order correction are first tested for the range of low Reynolds numbers simulated, and then used to predict the friction velocity and stress direction at the surface for flows at arbitrary Reynolds number. A model for the variation of these quantities with latitude and wind angle is also proposed which gives an acceptable fit to the simulation results. No large-scale longitudinal vortices are found in the velocity fields, reinforcing the conjecture that unstable thermal stratification, in addition to inflectional instability, is required to produce and maintain the large-scale rolls observed in the Earth's boundary layer. Comparisons of the Ekman layer with a related three-dimensional boundary layer reveal similarities of the mean profiles, as well as qualitative differences.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 213 , April 1990 , pp. 313 - 348
Copyright
© 1990 Cambridge University Press

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References

Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1983 Improved turbulence models based on large eddy simulation of homogeneous, incompressible, turbulent flows. Ph.D. dissertation, Mech. Engng Dept, Stanford University. Thermosci. Div. Rep TF-19.
Bradshaw, P. 1973 Effects of streamline curvature on turbulent flow. AGARD-AG-169.Google Scholar
Bradshaw, P. & Pontikos, N. S. 1985 Measurements in the turbulent boundary layer on an ‘infinite’ swept wing. J. Fluid Mech. 159, 105–130.Google Scholar
Brown, R. A. 1974 Analytical Methods in Planetary Boundary-layer Modelling. Wiley and Sons.
Caldwell, D. R. & Van Atta, C. W. 1970 Characteristics of Ekman boundary layer instabilities. J. Fluid Mech. 44, 79–95.Google Scholar
Caldwell, D. R., Van Atta, C. W. & Helland, K. N. 1972 A laboratory study of the turbulent Ekman layer. Geophys. Fluid Dyn. 3, 125–160.Google Scholar
Coles, D. E. 1968 The young person's guide to the data. Proc. AFOSR-IFP-Stanford conf. on computation of turbulent boundary layers, Stanford, CA, 18–25 Aug. 1968.Google Scholar
Csanady, G. T. 1967 On the ‘resistance law’ of a turbulent Ekman layer. J. Atmos. Sci. 24, 467–471.Google Scholar
Deardorff, J. W. 1970 A three-dimensional numerical investigation of the idealized planetary boundary layer. Geophys. Fluid Dyn. 1, 377–410.Google Scholar
Deardorff, J. W. 1972 Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci. 29, 91–115.Google Scholar
Etling, D. & Wippermann, F. 1975 On the instability of a planetary boundary layer with Rossby number similarity. Boundary-layer Met. 9, 341–360.Google Scholar
Faller, A. J. 1963 An experimental study of the instability of the laminar Ekman boundary layer. J. Fluid Mech. 15, 560–576.Google Scholar
Faller, A. J. 1965 Large eddies in the atmospheric boundary layer and their possible role in the formation of cloud rows. J. Atmos. Sci. 22, 176–184.Google Scholar
Johnston, J. P., Halleen, R. M. & Lezius, D. K. 1972 Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533–557.Google Scholar
Leibovich, S. & Lele, S. K. 1985 The influence of the horizontal component of Earth's angular velocity on the instability of the Ekman layer. J. Fluid Mech. 150, 41–87.Google Scholar
Le Mone, M. A. 1973 The structure and dynamics of horizontal roll vortices in the planetary boundary layer. J. Atmos. Sci. 30, 1077–1091.Google Scholar
McBean, G. A. (ed.) 1979 The planetary boundary layer. WMO no. 530, Tech. Note no. 165.
Mason, P. J. & Thomson, D. J. 1987 Large-eddy simulations of the neutral-static-stability planetary boundary layer. Q. J. R. Met. Soc. 113, 413–443.Google Scholar
Melander, M. V. 1983 An algorithmic approach to the linear stability of the Ekman layer. J. Fluid Mech. 132, 283–293.Google Scholar
Spalart, P. R. 1986a Numerical simulation of boundary layers. Part 1. Weak formulation and numerical method. NASA TM 88222.Google Scholar
Spalart, P. R. 1986b Numerical study of sink-flow boundary layers. J. Fluid Mech. 172, 307–328.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R = 1410. J. Fluid Mech. 187, 61–98.Google Scholar
Spalart, P. R. 1989 Theoretical and numerical study of a three-dimensional turbulent boundary layer. J. Fluid Mech. 205, 319–340.Google Scholar
Tatro, P. R. & Mollo-Christensen, E. L. 1967 Experiments on Ekman layer instability. J. Fluid Mech. 28, 531–543.Google Scholar
Tennekes, H. 1982 Chapter 2 of Atmospheric Turbulence and Air Pollution Modelling (ed. F. T. M. Nieuwstadt & H. Van Dop). Reidel.
Tritton, D. J. 1978 Turbulence in rotating fluids. In Rotating Fluids in Geophysics (ed. P. H. Roberts & A. M. Soward). Academic Press.
Wippermann, F. K., Etling, D. & Kirstein, H. J. 1978 On the instability of a planetary boundary layer with Rossby number similarity. Boundary-Layer Met. 15, 301–321.Google Scholar
Wyngaard, J. C., Cote, O. R. & Rao, K. S. 1974 Modeling the atmospheric boundary layer. In Turbulent Diffusion in Environmental Pollution, vol. 18A (ed. F. N. Frenkiel & R. E. Munn). Academic Press.