Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-28T07:17:29.376Z Has data issue: false hasContentIssue false
  • English
  • Français

The deepening of a mixed layer in a stratified fluid

Published online by Cambridge University Press:  29 March 2006

P. F. Linden
P. F. Linden
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper two aspects of the deepening of a mixed layer in a stratified fluid are examined in the laboratory. The first is the deepening of a layer into a region of constant density gradient. Turbulence is produced by an oscillating grid which generates a horizontally homogeneous field of motion with no significant mean flow. It is found that the rate at which the potential energy of the basic stratification is increased by the mixing does not bear a simple relationship to the rate of energy input by the grid. On the other hand, when allowance is made for the decay of turbulent energy away from the grid and only that portion to reach the bottom of the mixed layer is considered, the rate of potential energy increase is found to be proportional to this available energy. The second aspect to be discussed is the effect of energy radiation by internal waves in the region below the mixed layer. Estimates are made of the possible loss of energy to these waves, which reduces the amount available to deepen the layer. An experimental demonstration of up to 50 % reduction in the mixing rate due to the presence of internal waves is given. Finally, the implications of these results are discussed in the light of current theoretical models of the deepening process.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 2 , 23 September 1975 , pp. 385 - 405
Copyright
© 1975 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

Bouvard, M. & Dumas, H. 1967 Measurements of turbulence in water by the hot wire method. Houille Blanche, 22, 257–27.Google Scholar
Carson, D. J. 1973 The development of a dry inversion-capped convectively unstable boundary layer. Quart. J. Roy. Met. Soc. 99, 450–467Google Scholar
Crapper, P. F. & Linden, P. F. 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–64Google Scholar
Denman, L. K. & Miyake, M. 1973 Upper layer modification at Ocean Station Papa: observations and simulation. J. Phys. Oceanog. 3, 185–196Google Scholar
Kato, H. & Phillips, O. M. 1969 On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 643–655Google Scholar
Kitaigorodskii, S. A. & Miropol'Skii, Yu. Z. 1970 Theory of the upper quasihomogeneous layer and seasonal thermocline in the open ocean. Izv. Atmos. Ocean. Phys. 6, 97–102Google 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, 467–480Google Scholar
Niiler, P. P. 1975 Deepening of the wind-mixed layer. Submitted to J. Mar. Res.Google Scholar
Thompson, S. M. & Turner, J. S. 1975 Mixing across an interface due to turbulence generated by an oscillating grid. J. Fluid Mech. 67, 349–368Google Scholar
Thorpe, S. M. 1966 Internal gravity waves. Ph.D. thesis, University of Cambridge
Thorpe, S. M. 1973 Turbulence in stably stratified fluids: a review of laboratory experiments. Boundary-Layer Met. 5, 95–119Google Scholar
Townsend, A. A. 1966 Internal waves produced by a convective layer. J. Fluid Mech. 24, 307–319Google Scholar
Turner, J. S. 1968 The influence of molecular diffusivity on turbulent entrainment across a density interface. J. Fluid Mech. 33, 639–656Google Scholar