Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-09T22:00:43.459Z Has data issue: false hasContentIssue false
  • English
  • Français

A boundary layer topped by a density interface

Published online by Cambridge University Press:  20 April 2006

J.-F. Piat  and
E. J. Hopfinger
J.-F. Piat
Affiliation:
Institut de Méanique (Laboratoire associé au C.N.R.S.). Université de Grenoble, France Present address: Onera, 73500, Modane, France.
E. J. Hopfinger
Affiliation:
Institut de Méanique (Laboratoire associé au C.N.R.S.). Université de Grenoble, France
Get access Rights & Permissions [Opens in a new window]

Abstract

A rough-wall turbulent boundary layer which grows into a temperature interface situated at the outer edge is investigated experimentally. Reynolds numbers based on boundary-layer thickness δ range from 4 × 103 to 104. Overall Richardson numbers Ri*, defined in terms of the friction velocity and the boundary-layer thickness, are in the range 0 ≤ Ri* [lsim ] 80. Measurements of the mean profiles and of the variances of the velocity fluctuations show that the interface acts in some respects like a moving wall: the velocity profile tends towards a turbulent Couette-type profile and the longitudinal r.m.s. turbulent velocity begins to be amplified at the base of the interfacial layer and reaches a maximum in about the centre. Time-lag correlations of fluctuating quantities taken just above the centre of the interfacial layer have a behaviour characteristic of internal waves, namely a 90° phase lag between vertical velocity and temperature fluctuations. These waves occur as short wave packets and propagate mainly horizontally. On the base of the interface the correlations exhibit the usual symmetric behaviour.

The normalized entrainment velocity ue/u* decreases when Ri* increases but does not follow a power law in Ri*. This is consistent with momentum balance, which indicates that ue/u* also depends on the mean-flow Richardson number Ri0 = gΔTδ/TU02 and on the change in momentum and temperature defect. Momentum balance also shows that, when the undisturbed flow has zero pressure gradient, the boundary layer is expected to separate owing to entrainment when Ri0 ≅ 0.5

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 113 , December 1981 , pp. 411 - 432
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

Armi, L. 1977 Effects of density stratification on turbulence. WHOI Summer Program, p. 65, ref. no. 77–64.
Arya, S. P. S. 1975 Buoyancy effects in a horizontal flat-plate boundary layer. J. Fluid Mech. 68, 321–343.Google Scholar
Crapper, P. F. & Linden, P. F. 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–63.Google Scholar
Gartrell, G. 1979 Studies on the mixing in a density-stratified shear flow. Ph.D. thesis, California Institute of Technology.
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Hopfinger, E. J. 1973 Development of a stratified turbulent, shear flow. In Proc Int. Symp. Stratified Flows, Novosibirsk, 1972, A.S.C.E. Publication.
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
Hunt, J. C. R. & Graham, J. M. R. 1978 Free-stream turbulence near plane boundaries. J. Fluid Mech. 84, 209–235.Google Scholar
Kantha, L. H., Phillips, O. M. & Azad, R. S. 1977 On turbulent entrainment at a stable density interface. J. Fluid Mech. 79, 753–768.Google Scholar
Kato, H. & Phillips, O. M. 1969 On the penetration of a turbulent layer into a stratified fluid. J. Fluid Mech. 37, 643–655.Google Scholar
Koop, C. G. & Browand, F. K. 1979 Instability and turbulence in a stratified fluid with shear. J. Fluid Mech. 93, 135–159.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
Lofquist, K. 1960 Flow and stress near an interface between stratified liquids. Phys. Fluids 3, 158–175.Google Scholar
Mcdougall, T. J. 1979 Measurements of turbulence in a zero-mean-shear mixed layer. J. Fluid Mech. 94, 409–431.Google Scholar
Nicholl, C. I. H. 1970 Some dynamical effects of heat on a turbulent boundary layer. J. Fluid Mech. 40, 361–384.Google Scholar
Niiler, P. P. & Kraus, E. B. 1977 One dimensional models of the upper ocean. In Modelling and Prediction of the Upper Layers of the Ocean (ed. E. B. Kraus). Pergamon.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Piat, J.-F. 1979 Pénétration d'une couche limite turbulente dans une interface de densité. Thèse de Docteur-Ingénieur, Université de Grenoble.
Price, J. F. 1979 On the scaling of stress-driven entrainment experiments. J. Fluid Mech. 90, 509–529.Google Scholar
Robertson, J. M. & Johnson, H. F. 1970 Turbulence structure in plane Couette flow. Proc. A.S.C.E. 96 (EM6), 1171–1182.Google Scholar
Schlichting, H. 1960 Boundary Layer Theory, 4th edn. McGraw-Hill.
Schon, J. P. & Baille, A. 1972 Méthode d'isolement des fluctuations turbulentes cinématiques et thermiques au moyen d'une sonde anémométrique à trois fils. C.r. Acad. Sci. Paris 274, 116–000.Google Scholar
Thomas, N. H. & Hancock, P. E. 1977 Grid turbulence near a moving wall. J. Fluid Mech. 82, 481–486.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
Uzkan, T. & Reynolds, W. C. 1967 A shear-free turbulent boundary layer. J. Fluid Mech. 28, 803–821.Google Scholar