Skip to main content
×
Home

Direct numerical simulations of the effects of shear on turbulent Rayleigh-Bénard convection

  • J. Andrzej Domaradzki (a1) and Ralph W. Metcalfe (a2)
Abstract

The interaction between shear and buoyancy effects for Bénard convection in plane Couette flow is studied by performing direct numerical simulations. At moderate Rayleigh number (≈10000−50000), shear tends to organize the flow into quasi-two-dimensional rolls parallel to the mean flow and can enhance heat transfer, while at higher Rayleigh number (>150000), shear tends to disrupt the formation of convective plumes and can reduce heat transfer. A significant temporal oscillation in the local Nusselt number was consistently observed at high Rayleigh numbers, a factor that may contribute to the scatter seen in experimental data. This effect, plus the time-varying reversal of the mean temperature gradient in the middle of the channel, is consistent with a flow model in which the dynamics of large-scale, quasi-two-dimensional, counter-rotating vortical cells are alternately driven by buoyancy and inertial effects. An analysis of the energy balance in the flow shows that the conservative pressure diffusion term, which has been frequently neglected in turbulence models, plays a very important dynamical role in the flow evolution and should be more carefully modelled. Most of the turbulent energy production due to mean shear is generated in the boundary layers, while the buoyant production occurs mainly in the relatively uniform convective core. The simulations and the laboratory experiments of Deardorff & Willis (1967) are in very reasonable qualitative agreement, suggesting that the basic dynamics of the flow are being accurately simulated.

Copyright
References
Hide All
Ahlers, G. & Behringer, R. P. 1978 Evolution of turbulence from the Rayleigh-Bénard instability. Phys. Rev. Lett. 40, 712716.
Bergé, P. & Dubois, M. 1976 Time dependent velocity in Rayleigh-Bénard convection: a transition to turbulence. Optics Commun. 19, 129133.
Brown, W. 1973 Heat-flux transitions at low Rayleigh number. J. Fluid Mech. 60, 539559.
Busse, F. H. 1972 The oscillatory instability of convection rolls in a low Prandtl number fluid. J. Fluid Mech. 52, 97112.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon.
Chu, T. Y. & Goldstein, R. J. 1973 Turbulent convection in a horizontal layer of water. J. Fluid Mech. 60, 141159.
Clever, R. M. & Busse, F. H. 1974 Transition to time-dependent convection. J. Fluid Mech. 65, 625645.
Clever, R. M. & Busse, F. H. 1977 Instabilities of longitudinal convection rolls in an inclined layer. J. Fluid Mech. 81, 107127.
Clever, R. M., Busse, F. H. & Kelly, R. E. 1977 Instabilities of longitudinal convection rolls in Couette flow. Z. angew. Math. Phys. 28, 771783.
Constantin, P., Foias, C., Manley, O. P. & Teman, R. 1985 Determining modes and fractal dimension of turbulent flows. J. Fluid Mech. 150, 427440.
Curry, J. H., Herring, J. R., Loncaric, J. & Orszag, S. A. 1984 Order and disorder in two-and three-dimensional Bénard convection. J. Fluid Mech. 147, 138.
Daly, B. J. 1974 A numerical study of turbulence transitions in convective flow. J. Fluid Mech. 64, 129165.
Deardorff, J. W. 1970 A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J. Fluid Mech. 41, 453480.
Deardorff, J. W. 1973 Three-dimensioinal modeling of the planetary boundary layer. In Workshop in Micrometeorology (ed. D. A. Haugen), p. 271. American Meteorology Society.
Deardorff, J. W. & Willis, G. E. 1967 Investigation of turbulent thermal convection between horizontal plates. J. Fluid Mech. 28, 675704.
Deardorff, J. W. & Willis, G. E. 1985 Furhter results from a laboratory model of the convective planetary boundary layer. Boundary-Layer Met. 32, 205236.
Dubois, M. & Bergé, P. 1978 Experimental study of the velocity field in Rayleigh-Bénmard convection. J. Fluid Mech. 85, 641653.
Eidson, T. M. 1985 Numerical simulation of the turbulent Rayleigh-Bénard problem using subgrid modelling. J. Fluid Mech. 158, 245268.
Eidson, T. M., Hussaini, M. Y. & Zang, T. a. 1986 Simulation of the turbulent Rayleigh-Bénard problem using a spectral/finite difference technique. ICASE Rep. 86-6.
Goldstein, R. J. & Chu, T. Y. 1969 Thermal convection in ahorizontal layer of air. Prog. Heat Mass Transfer 2, 55.
Gollub, J. P., Hulbert, S. L., Dolny, G. M. & Swinney, H. L. 1977 In Proton Correlation Spectroscopy (ed. F. Cummins & E. R. Pike). Plenum.
Gottlieb, D., Hussaini, M. Y. & Orszag, S. A. 1984 Theory and application of spectral methods. In Spectral Methods for Partial Differential Equations ed. R. G. Voigt, D. Gottlieb & M. Y. Hussaini), pp. 154. SIAM.
Grötzbach, G. 1983 Spatial resoloution for direct numerical simulation of the Rayleigh-Bénard convection. J. Comp. Phys. 49, 241264.
Hart, J. E. 1971 Stability of the flowin differentially heated inclined box. J. Fluid Mech. 47, 547576.
Hathaway, D. A. & Somerville, R. C. J. 1986 Nonlinear interactions between convection, rotation and flows with vertical shear. J. Fluid Mech. 164, 91105.
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Howard, L. N. 1964 Convection at High Rayleigh numbers. In Proc. Eleventh Intl Congr. Applied Mechanics, Münich (ed. Görtler, H.), pp. 11091115. Springer.
Ingersoll, A. P. 1966 Thermal convection with shear at high Rayleigh number. J. Fluid Mech. 25, 209228.
Krishnamurti, R. 1970a On the transition to turbulent convection. Part 1. The transition from two-to three-dimensional flow., J. Fluid Mech. 42, 295307.
Krishnamurti, R. 1970b On the transition to turbulent convection. Part 2. The transition from time-dependent flow. J. Fluid Mech. 42, 309320.
Krishnamurti, R. 1973 Some further studies on the transition to turbulent convection. J. Fluid Mech. 60, 285303.
Kuo, H. L. 1963 Perturbations of plane Couette flow in stratified fluid and origin of cloud streets. Phys. Fluids 6, 195211.
Lipps, F. B. 1971 Two-dimensional numerical experiments in thermal convection with vertical shear. J. Atmos. Sci. 28, 319.
Lipps, F. B. 1976 Numerical simulation of three-dimensional Bénard convection in air. J. Fluid Mech. 75, 113148.
Lipps, F. B. & Somerville, R. C. J. 1971 Dynamics of variable wavelength in finite-amplitude Bénard convection. Phys. Fluids 14, 759765.
Malkus, W. V. R. 1954 Discrete transitions in turbulent convection.. Proc. R. Soc. Lond. A 225, 196212.
Manley, O. P. & Treve, Y. M. 1981 Minimum number of modes in approximate solutions to equations of hydrodynamics. Phys. Lett. 82A, 8890.
Marcus, P. S. 1984 Simulation of Taylor-Couette flow. Part 1. Numerical methods and comparison with experiment. J. Fluid Mech. 146, 4564.
McLaughlin, J. B. & Orszag, S. A. 1982 Transition from periodic to chaotic thermal convection. J. Fluid Mech. 122, 123142.
Mellor, G. L. & Yamada, T. 1982 Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys. 20, 851875.
Monin, A. S. & Yaglom, A. M. 1979 Statistical Fluid Mechanics, Vol. 1. MIT Press.
Orszag, S. A. & Kells, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159205.
Richter, F. M. & Parsons, B. 1975 On the interaction of two scales of convection in the mantle. J. Geophys. Res. 80, 25292541.
Rossby, T. 1969 A study of Bénard convection with and without rotation. J. Fluid Mech. 36, 309335.
Schlüter, A., Lortz, D. & Busse, F. 1965 On the stability of steady finite amplitude convection. J. Fluid Mech. 44, 661672.
Sparrow, E. M. & Husar, R. B. 1969 Longitudinal vortices in natural convection flow on inclined plates. J. Fluid Mech. 37, 251255.
Threlfall, D. C. 1975 Free convection in low-temperature gaseous helium. J. Fluid Mech. 67, 1728.
Townsend, A. A. 1959 Temperature fluctuations over a heated horizontal surface. J. Fluid Mech. 5, 209241.
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.
Veronis, G. 1966 Large amplitude Bénard convection. J. Fluid Mech. 26, 4968.
Willis, G. e. & Deardorff, J. W. 1965 Measurements on the development of thermal turbulence in air between horizontal plates. Phys. Fluids 8, 2225.
Willis, G. E. & Deardorff, J. W. 1970 The oscillatory motions of Rayleigh convection. J. Fluid Mech. 44, 661672.
Willis, G. E., Deardorff, J. W. & Somerville, R. C. J. 1972 Roll-diameter dependence in Rayleigh convection and its effect upon heat flux. J. Fluid Mech. 54, 351367.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 46 *
Loading metrics...

Abstract views

Total abstract views: 148 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd November 2017. This data will be updated every 24 hours.