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Buoyancy effects in a horizontal flat-plate boundary layer

Published online by Cambridge University Press:  29 March 2006

S. P. S. Arya
Affiliation:
Department of Atmospheric Sciences, University of Washington, Seattle

Abstract

Observations made in a well-developed, thermally stratified, horizontal, flat- plate boundary layer are used to study the effects of buoyancy on the mean flow and turbulence structure. These are represented in a similarity framework obtained from the concept of local equilibrium in a fully developed turbulent flow. Mean velocity and temperature profiles in both the inner and outer layers are strongly dependent on the thermal stratification, the former suggesting an increase in the thickness of the viscous sublayer with increasing stability. The coefficients of skin friction and heat transfer, on the other hand, decrease with increasing stability.

Normalized turbulent intensities, fluxes and their correlation coefficients also vary with buoyancy. In stable conditions, turbulence becomes rapidly suppressed with increasing stability as more and more energy has to be expended in over- coming buoyancy forces. The buoyancy effects are found to be more dominant in the stress budget than in the turbulent energy budget. The horizontal heat flux is much greater than the vertical heat flux and their ratio increases with stability. The ratio of the eddy diffusivities of heat and momentum, on the other hand, decreases with increasing stability. The spectra of velocity and temperature fluctuations indicate no buoyancy subrange, but the wavenumber corresponding to peak energy is found to increase with increasing stability.

Type
Research Article
Copyright
© 1975 Cambridge University Press

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References

Arya, S. P. S. 1968 Structure of stably stratified turbulent boundary layer. Ph.D. dissertation, Colorado State University, Fort Collins.
Arya, S. P. S. 1972a The critical condition for the maintenance of turbulence in stratified flows. Quart. J. Roy. Met. Soc. 90, 264273.Google Scholar
Arya, S. P. S. 1972 Free convection similarity and measurements in flows with and without shear. J. Atmos. Sci. 29, 877885.Google Scholar
Arya, S. P. S. 1975 Geostrophic drag and heat transfer relations for the atmospheric boundary layer. Quart. J. Roy. Met. Soc. 101 (to appear).Google Scholar
Arya, S. P. S. & Plate, E. J. 1969a Hot-wire measurements in non-isothermal flow. Instrum. & Control Syst. 42, 8790.Google Scholar
Arya, S. P. S. & Plate, E. J. 1969b Modeling of the stably stratified atmospheric boundary layer. J. Atmos. Sci. 26, 656665.Google Scholar
Blom, J. 1970 An experimental determination of the turbulent Prandtl number in a developing temperature boundary layer. Ph.D. dissertation, Technological University, Eindhoven, Netherlands.
Bolciano, R. 1959 Turbulent spectra in a stably stratified atmosphere. J. Geophys. Res. 64, 22262229.Google Scholar
Bradshaw, P. 1967 The turbulence structure of equilibrium boundary layers. J. Fluid Mech. 29, 625645.Google Scholar
Brundrett, E. & Burroughs, P. R. 1967 The temperature inner-law and heat transfer for turbulent air flow in a vertical square duct. Int. J. Heat Mass Transfer, 10, 11331142.Google Scholar
Businger, J. A., Wyngaard, J. C., Izumi, Y. & Bradley, E. F. 1971 Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci. 28, 181189.Google Scholar
Carl, D. M., Tarbell, T. C. & Panofsky, H. A. 1973 Profiles of wind and temperature from towers over homogeneous terrain. J. Atmos. Sci. 30, 788794.Google Scholar
Cermax, J. E., Sandborn, V. A., Plate, E. J., Binder, G. H., Chuang, H., Meroney, R. N. & ITO, S. 1966 Simulation of atmospheric motion by wind-tunnel flows. Tech. Rep. Fluid Dyn. & Diffusion Lab., Colorado State University, Fort Collins, no. 17.Google Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. in Appl. Mech., 4, 151.Google Scholar
Deardorff, J. W. 1972 Numerical investigation of neutral and unstable planetary boundary layers. J. Atmos. Sci. 29, 91115.Google Scholar
Deardorff, J. W. & Willis, G. E. 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28, 675704.Google Scholar
Ellison, T. H. 1957 Turbulent transport of heat and momentum from an infinite rough plane. J. Fluid Mech. 2, 456466.Google Scholar
Ellison, T. H. & Turner, J. S. 1960 Mixing of dense fluid in a turbulent pipe flow. J. Fluid Mech. 8, 514544.Google Scholar
Hinze, J. O. 1959 Turbulence. McGraw-Hill.
Kader, B. A. & Yaglom, A. M. 1972 Heat and mass transfer laws for fully turbulent wall flows. Int. J. Heat Mass Transfer, 15, 23292353.Google Scholar
Kestin, J. & Persen, L. N. 1962 Application of Schmidt's method to the calculation of Spalding function and of the skin-friction coefficient in turbulent flow. Int. J. Heat Mass Transfer, 5, 143152.Google Scholar
Kraus, E. B. 1972 Atmosphere-Ocean Interaction. Oxford University Press.
Lewellen, W. S. & Tesxe, M. 1973 Prediction of the Monin-Obukhov similarity functions from an invariant model of turbulence. J. Atmos. Sci. 30, 13401345.Google Scholar
Lumley, J. L. 1964 The spectrum of nearly inertial turbulence in a stable stratified fluid. J. Atmos. Sci. 21, 99102.Google Scholar
Lumley, J. L. 1967 Theoretical aspects of research in turbulence in stratified flows. In Atmospheric Turbulence and Radiowave Propagation, pp. 105110. Moscow: Nauka.
Lumley, J. L. & Panofsxy, H. A. 1964 The Structure of Atmospheric Turbulence. Inter-science.
Mellor, G. L. 1973 Analytic prediction of the properties of stratified planetary surface layers. J. Atmos. Sci. 30, 10611069.Google Scholar
Mery, P., Schon, J. P & Solal, J. 1974 Comparison of thermally neutral and unstable shear flows in the wind tunnel and the atmosphere. Adv. in Geophys. B 18 (to appear).Google Scholar
Monin, A. S. 1962 Empirical data on turbulence in the surface layer of the atmosphere. J. Geophys. Res. 67, 31033109.Google Scholar
Monin, A. S. 1965 On the symmetry properties in the surface layer of air. Izv. Atmos. Oceanic Phys., Acad. Sci. U.S.S.R. 1, 2530 (English trans.).Google Scholar
Monin, A. S. & Oboukhov, A. M. 1954 Basic regularity in turbulent mixing in the surface layer of the atmosphere. Trans. Geophys. Inst., Acad. Sci. U.S.S.R., no. 24 (151), pp. 163187.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics: The Mechanics of Turbulence. M.I.T. Press.
Nicholl, C. H. I. 1970 Some dynamical effects of heat on a turbulent boundary layer.
Phillips, O. M. 1967 On the Bolgiano and Lumley-Shur theories of the buoyant subrange. In Atmospheric Turbulence and Radiowave Propagation, pp. 121128. Moscow: Nauka.
Plate, E. J. & Arya, S. P. S. 1969 Turbulence spectra in a stably stratified boundary layer. Radio Sci. 4, 11631168.Google Scholar
Plate, E. J. & Cermak, J. E. 1963 Micrometeorological wind tunnel facility: description and characteristics. Fluid Dyn. & Diffusion Lab., Colorado State University, Fort Collins, Rep. CER63EJP-JEC 9.Google Scholar
Rotta, J. C. 1962 Turbulent boundary layers in incompressible flow. Prog. Aero. Sci. 2, 1219.Google Scholar
Stewart, R. W. 1959 The problem of diffusion in a stratified fluid. Adv. in Geophys. 6, 303311.Google Scholar
Townsend, A. A. 1958 Turbulent flow in a stably stratified atmosphere. J. Fluid Mech. 5, 361372.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Webb, E. K. 1970 Profile relationships: the log-linear range and extension to strong stability. Quart. J. Roy. Met. Soc. 96, 6790.Google Scholar
Weseley, M. L., Thurtell, G. W. & Tanner, C. B. 1970 Eddy correlation measurements of sensible heat flux near the earth's surface. J. Appt. Meteor. 9, 4550.Google Scholar
Wyngaard, J. C., COT, O. R. & Izumi, Y. 1971 Local free convection, similarity, and the budgets of shear stress and heat flux. J. Atmos. Sci. 28, 11711182.Google Scholar
Wyngaard, J. C., Coté, O. R. & RAO, K. S. 1974 Modeling of the atmospheric boundary layer. Adv. in Geophys. A 18 (to appear).Google Scholar
Zilitinkevich, S. S. & Chalipov, D. V. 1968 Determining the universal wind-velocity and temperature profiles in the atmospheric boundary layer. Izv. Atmos. Ocean. Phys., Acad. Sci. U.S.S.R. 4, 165169 (English trans.).Google Scholar
Zilitinkevich, S. S., Laikhtman, D. L. & Monin, A. S. 1967 Dynamics of the atmospheric boundary layer. Izv. Atmos. Ocean. Phys., Acad. Sci. U.S.S.R. 3, 170191(English trans.).Google Scholar
Zubpovski, S. L. & Twang, L. R. 1966 Horizontal turbulent heat flow. Izv. Atmos. Ocean. Phys., Acad. Sci. U.S.S.R. 2, 798799 (English trans.).Google Scholar