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Turbulent natural convection along a vertical plate immersed in a stably stratified fluid

Published online by Cambridge University Press:  25 September 2009

EVGENI FEDOROVICH  and
ALAN SHAPIRO
EVGENI FEDOROVICH*
Affiliation:
School of Meteorology, University of Oklahoma, 120 David L. Boren Blvd, Norman, OK 73072-7307, USA
ALAN SHAPIRO
Affiliation:
School of Meteorology, University of Oklahoma, 120 David L. Boren Blvd, Norman, OK 73072-7307, USA
*
†Email address for correspondence: fedorovich@ou.edu
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Abstract

The paper considers the moderately turbulent natural convection flow of a stably stratified fluid along an infinite vertical plate (wall). Attention is restricted to statistically stationary flow driven by constant surface forcing (heating), with Prandtl number of unity. The flow is controlled by the surface energy production rate Fs, molecular viscosity/diffusivity ν and ambient stratification in terms of the Brunt–Väisälä (buoyancy) frequency N. Following the transition from a laminar to a turbulent regime, the simulated flow enters a quasi-stationary oscillatory phase. In this phase, turbulent fluctuations gradually fade out with distance from the wall, while periodic laminar oscillations persist over much larger distances before they fade out. The scaled mean velocity, scaled mean buoyancy and scaled second-order turbulence statistics display a universal behaviour as functions of distance from the wall for given value of dimensionless combination Fs/(νN2) that may be interpreted as an integral Reynolds number. In the conducted numerical experiments, this number varied in the range from 2000 to 5000.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 636 , 10 October 2009 , pp. 41 - 57
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Armfield, S. W. & Patterson, J. C. 1992 Wave properties of natural convection boundary layers. J. Fluid Mech. 239, 195–211.CrossRefGoogle Scholar
Armfield, S. W., Patterson, J. C. & Lin, W. 2007 Scaling investigation of the natural convection boundary layer on an evenly heated plate. Intl J. Heat Mass Transfer 50, 1592–1602.CrossRefGoogle Scholar
Bergholz, R. F. 1978 Instability of steady natural convection in a vertical fluid layer. J. Fluid Mech. 84, 743–768.CrossRefGoogle Scholar
Boudjemadi, R., Mapu, V., Laurence, D. & Le Quere, P. 1997 Budgets of turbulent stresses and fluxes in a vertical slot natural convection flow at Rayleigh Ra = 105 and 5.4⋅105. Intl J. Heat Fluid Flow 18, 70–79.CrossRefGoogle Scholar
Cushman-Roisin, B. 1994 Introduction to Geophysical Fluid Dynamics. Prentice Hall.Google Scholar
Daniels, P. G. & Patterson, J. C. 1997 On the long-wave instability of natural-convection boundary layers. J. Fluid Mech. 335, 57–73.CrossRefGoogle Scholar
Daniels, P. G. & Patterson, J. C. 2001 On the short-wave instability of natural convection boundary layers. Proc. R. Soc. Lond. A 457, 519–538.CrossRefGoogle Scholar
Fedorovich, E., Conzemius, R., Esau, I., Katopodes Chow, F., Lewellen, D., Moeng, C.-H., Pino, D., Sullivan, P. & Vilà-Guerau de Arellano, J. 2004 a Entrainment into sheared convective boundary layers as predicted by different large eddy simulation codes. In Sixteenth Symposium on Boundary Layers and Turbulence, (Am. Meteor. Soc., 9–13 August), Portland, Maine, CD-ROM.Google Scholar
Fedorovich, E., Conzemius, R. & Mironov, D. 2004 b Convective entrainment into a shear-free linearly stratified atmosphere: bulk models reevaluated through large eddy simulations. J. Atmos. Sci. 61, 281–295.2.0.CO;2>CrossRefGoogle Scholar
Fedorovich, E., Nieuwstadt, F. T. M. & Kaiser, R. 2001 Numerical and laboratory study of horizontally evolving convective boundary layer. Part I: Transition regimes and development of the mixed layer. J. Atmos. Sci. 58, 70–86.2.0.CO;2>CrossRefGoogle Scholar
Gebhart, B., Jaluria, Y., Mahajan, R. L. & Sammakia, B. 1988, Buoyancy-Induced Flows and Transport. Hemisphere Publishing.Google Scholar
George, W. K. & Capp, S. P. 1979 A theory for natural convection turbulent boundary layers next to heated vertical surfaces. Intl J. Heat Mass Transfer 22, 813–826.CrossRefGoogle Scholar
Gill, A. E. & Davey, A. 1969 Instabilities of a buoyancy-driven system. J. Fluid Mech. 35, 775–798.CrossRefGoogle Scholar
Langhaar, H. L. 1951 Dimensional Analysis and Theory of Models. Robert E. Krieger Publishing Company.Google Scholar
Park, J. S. 2001 Transient buoyant flows of a stratified fluid in a vertical channel. KSME Intl J. 15, 656–664.CrossRefGoogle Scholar
Park, J. S. & Hyun, J. M. 1998 Transient behaviour of vertical buoyancy layer in a stratified fluid, Intl J. Heat Mass Transfer 41, 4393–4397.CrossRefGoogle Scholar
Phillips, J. R. 1996 Direct simulations of turbulent unstratified natural convection in a vertical slot for (Pr = 0.71). Intl J. Heat Mass Transfer 39, 2485–2494.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Shapiro, A. & Fedorovich, E. 2004 a Prandtl-number dependence of unsteady natural convection along a vertical plate in a stably stratified fluid. Intl J. Heat Mass Transfer 47, 4911–4927.CrossRefGoogle Scholar
Shapiro, A. & Fedorovich, E. 2004 b Unsteady convectively driven flow along a vertical plate immersed in a stably stratified fluid. J. Fluid Mech. 498, 333–352.CrossRefGoogle Scholar
Shapiro, A. & Fedorovich, E. 2006 Natural convection in a stably stratified fluid along vertical plates and cylinders with temporally-periodic surface temperature variations. J. Fluid Mech. 546, 295–311.CrossRefGoogle Scholar
Shchepetkin, A. F. & McWilliams, J. C. 1998 Quasi-monotone advection schemes based on explicit locally adaptive dissipation. Mon. Weather Rev. 126, 1541–1580.2.0.CO;2>CrossRefGoogle Scholar
Smyth, W. D. & Moum, J. N. 2000 Length scales of turbulence in stably stratified mixing layers. Phys. Fluids 12, 1327–1342.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. The MIT Press.CrossRefGoogle Scholar
Versteegh, T. A. M. & Nieuwstadt, F. T. M. 1998 Turbulent budgets of natural convection in an infinite, differentially heated, vertical channel. Intl J. Heat Fluid Flow 19, 135–149.CrossRefGoogle Scholar
Versteegh, T. A. M. & Nieuwstadt, F. T. M. 1999 A direct numerical simulation of natural convection between two infinite vertical differentially heated walls scaling laws and wall functions. Intl J. Heat Mass Transfer 42, 3673–3693.CrossRefGoogle Scholar