Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-18T23:51:08.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Penetrative convection at low Pélet number

Published online by Cambridge University Press:  20 April 2006

Richard A. Denton  and
Ian R. Wood
Richard A. Denton
Affiliation:
University of Canterbury, Christchurch, New Zealand Present address: Sonderforschungsbereich 80, University of Karlsruhe, 7500 Karlsruhe, West Germany.
Ian R. Wood
Affiliation:
University of Canterbury, Christchurch, New Zealand
Get access Rights & Permissions [Opens in a new window]

Abstract

A theoretical one-dimensional model of penetrative convection in a stable temperature stratification heated from below has been developed in which the partial derivatives of temperature with respect to height and time are assumed to be discontinuous at the interface. As a finite temperature gradient then exists immediately above the interface, molecular diffusion effects at low Pélet number can be included. The results of the numerical-analysis model are used to illustrate the relative contributions of molecular diffusion, interfacial turbulence and the ‘filling’ of the existing temperature stratification by the lower boundary heat flux. Data from low-Pélet-number experiments are used to verify the results of the theoretical model.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 113 , December 1981 , pp. 1 - 21
Copyright
© 1981 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adrian, R. J. 1975 Turbulent convection in water over ice. J. Fluid Mech. 69, 753–781.Google Scholar
Betts, A. K. 1973 Non-precipitating cumulus convection and its parameterization. Quart. J. Roy. Met. Soc. 99, 178–196.Google Scholar
Cattle, H. & Weston, K. J. 1975 Budget studies of heat flux profiles in the convection boundary layer over land. Quart. J. Roy. Met. Soc. 101, 353–363.Google Scholar
Crapper, P. F. & Linden, P. F. 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–63.Google Scholar
Deardorff, J. W. 1970 Convective velocity and temperature scales for the unstable planetary boundary layer and for Rayleigh convection. J. Atmos. Sci. 27, 1211–1213.Google Scholar
Deardorff, J. W. 1974 Three-dimensional numerical study of the height and mean structure of a heated planetary boundary layer. Boundary Layer Met. 7, 81–106.Google Scholar
Deardorff, J. W., Willis, G. E. & Lilly, D. K. 1969 Laboratory investigation of non-steady penetrative convection. J. Fluid Mech. 35, 7–31.Google Scholar
Denton, R. A. 1978 Entrainment by penetrative convection at low Péclet Number. Dept Civil Engng, Univ. Canterbury, Christchurch, N.Z., rep. no. 78/1.
Denton, R. A. & Wood, I. R. 1974 Convective motions and resulting entrainment in a two-layered fluid system heated from below. Conf. on Hydraulics and Fluid Mech., Christchurch, N.Z., vol. iii, pp. 361–368.
Farmer, D. M. 1975 Penetrative convection in the absence of mean shear. Quart. J. Roy. Met. Soc. 101, 869–891.Google Scholar
Heidt, F. D. 1977 The growth of a mixed layer in a stratified fluid. Boundary Layer Met. 12, 439–461.Google Scholar
Hopfinger, E. J. & Toly, J. A. 1976 Spatially decaying turbulence and its relation to mixing across density interfaces. J. Fluid Mech. 78, 155–175.Google Scholar
Howard, L. N. 1964 Convection at high Rayleigh number. Proc. 11th Int. Cong. Appl. Mech., Munich (ed. H. Görtler), pp. 1109–1115. Berlin: Springer.
Krishnamurti, R. 1970 On the transition to turbulent convection. 1. The transition from two to three dimensional flow. J. Fluid Mech. 42, 295–307.Google Scholar
Linden, P. F. 1973 The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60, 467–480.Google Scholar
Linden, P. F. 1975 The deepening of a mixed layer in a stratified fluid. J. Fluid Mech. 71, 385–405.Google Scholar
Munk, W. H. & Anderson, E. R. 1948 Notes on a theory of the thermocline. J. Marine Res. 7, 276–295.Google Scholar
Rouse, H. & Dodu, J. 1955 Diffusion turbulence à travers une discontinuité de densité. La Houille Blanche 10, 522–532.Google Scholar
Sparrow, E. M., Husar, R. B. & Goldstein, R. J. 1970 Observations and other characteristics of thermals. J. Fluid Mech. 41, 793–800.Google Scholar
Stull, R. B. 1973 Inversion rise model based on a penetrative convection. J. Atmos. Sci. 30, 1092–1099.Google Scholar
Stull, R. B. 1976 The energetics of entrainment across a density interface. J. Atmos. Sci. 33, 1260–1267.Google Scholar
Tennekes, H. 1973 A model for the dynamics of the inversion above a convective boundary layer. J. Atmos. Sci. 30, 558–567.Google Scholar
Thompson, S. & Turner, J. S. 1975 Mixing across an interface due to turbulence generated by an oscillating grid. J. Fluid Mech. 67, 349–368.Google Scholar
Townsend, A. A. 1964 Natural convection in water over an ice surface. Quart. J. Roy. Met. Soc. 90, 248–259.Google Scholar
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639–656.Google Scholar
Turner, J. S. 1973 Buoyancy effects in fluids. Cambridge University Press.
Willis, G. E. & Deardorff, J. W. 1974 A laboratory model of the unstable planetary boundary layer. J. Atmos. Sci. 31, 1297–1307.Google Scholar
Wolanski, E. J. & Brush, L. M. 1975 Turbulent entrainment across stable density step structures. Tellus, 27, 259–268.Google Scholar
Zilitinkevich, S. S. 1975 Comments on a ‘A Model for the dynamics of the inversion above a convective boundary layer’. J. Atmos. Sci. 32, 991–992.Google Scholar