Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-03T17:56:32.127Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical simulation of thermohaline convection in the upper ocean

Published online by Cambridge University Press:  19 April 2006

Victor E. Delnore
Victor E. Delnore*
Affiliation:
Department of Meteorology and Physical Oceanography, Cook College, Rutgers - The State University of New Jersey, New Brunswick, N.J. 08903
Get access Rights & Permissions [Opens in a new window]

Abstract

The intradiurnal heating and cooling cycle of the mixed layer of a tropical ocean is investigated through the use of a ‘pseudo-two-dimensional’ numerical model. Particular emphasis is given to two-component diffusion resulting from dynamic instabilities in the water column. The conservation equations for salt and heat include the effects of solar heating, horizontal advection and turbulent fluxes at the sea surface, while wind mixing enters through the use of depth-dependent eddy diffusion coefficients resulting from the wave-orbital shear model of Kitaigorodskiy (1961). All inputs are treated as functions of time of day, or calculated via the bulk aerodynamic method.

The entrainment fluxes of salt and heat due to the mechanical stirring of the wind and the fluxes due to molecular diffusion are treated as separate, their respective contributions being added to form the diffusion coefficients used in an alternating-direction explicit scheme to integrate the heat and salt equations. Near the surface, in the absence of strong solar heating (i.e. during the night), these two fluxes alone are insufficient to remove the near-surface static instabilities; thus the presence of some additional process is suggested. A dynamic stability analysis is carried out, based on the temperature and salinity gradients. The resulting Rayleigh numbers indicate the possibility of double-diffusive convection, whereby the vertical transfers of salt and heat may proceed at rates far greater than can be accounted for by molecular diffusion alone. Therefore, the molecular diffusions in the model are increased by a factor roughly proportional to the one-third power of the ratio of the local effective Rayleigh number to a critical Rayleigh number. The modified molecular diffusivities are then added to the eddy diffusion coefficients due to the wind, to form the total diffusion coefficients used in the numerical integrations.

Comparisons are made between the model-generated profiles of temperature and the profiles observed in the ocean. The comparisons show reasonable agreement in the diurnal cycle of the heat wave at 1 m vertical resolution (except for the model-generated surface layer being too deep during the late afternoon hours). (Previous models typically predict only the temperature and thickness of a homogeneous layer.) The results obtained with the model are instructive in estimating the relative importance of the various mixing processes in the upper ocean.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 96 , Issue 4 , 27 February 1980 , pp. 803 - 826
Copyright
Copyright © 1980 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.)

Footnotes

*

Present address: Kentron International, Inc., Hampton Technical Center, Hampton, Virginia 23666, U.S.A.

References

Crapper, P. F. & Linden, P. F. 1974 The structure of turbulent density interfaces. J. Fluid Mech. 65, 45–63CrossRefGoogle Scholar
Delnore, V. E. 1972 Diurnal variation of temperature and energy budget for the oceanic mixed layer during BOMEX. J. Phys. Oceanog. 2, 239–2472.0.CO;2>CrossRefGoogle Scholar
Delnore, V. E. & McHugh, J. 1972 BOMEX Period III Upper Ocean Soundings. Nat. Oceanic and Atmospheric Admin. Washington: U.S. Dept. of CommerceGoogle Scholar
Dietrich, G. 1963 General Oceanography. New York: InterscienceGoogle Scholar
Elliott, G. W. 1974 Precipitation signatures in sea surface layer conditions during BOMEX. J. Phys. Oceanog. 4, 498–5012.0.CO;2>CrossRefGoogle Scholar
Fofonoff, N. P. 1962 Physical properties of sea water. In The Sea (ed. Hill, M. N.), pp. 3–30. New York: InterscienceGoogle Scholar
Foster, T. D. 1971 A convective model for the diurnal cycle in the upper ocean. J. Geophys. Res. 76, 666–675CrossRefGoogle Scholar
Friedrich, H. & Levitus, S. 1972 An approximation to the equation of state for sea water, suitable for numerical models. J. Phys. Oceanog. 2, 514–5172.0.CO;2>CrossRefGoogle Scholar
Friehe, C. A. & Schmitt, K. F. 1976 Parameterization of air-sea interface fluxes of sensible heat and moisture by the bulk aerodynamic formulas. J. Phys. Oceanog. 6, 801–8092.0.CO;2>CrossRefGoogle Scholar
Gargett, A. E. 1976 An investigation of the occurrence of oceanic turbulence with respect to fine structure. J. Phys. Oceanog. 6, 139–1592.0.CO;2>CrossRefGoogle Scholar
Garwood, R. W. 1977 An oceanic mixed layer model capable of simulating cyclic states. J. Phys. Oceanog. 7, 455–4682.0.CO;2>CrossRefGoogle Scholar
Huppert, H. E. 1972 Double-diffusive convection. In Notes on the 1972 Summer Study Program in Geophysical Fluid Dynamics, vol. I. Ref. no. 72–79 (Unpublished manuscript) Woods Hole Oceanographic InstitutionGoogle Scholar
Huppert, H. E. & Turner, J. S. 1972 Double-diffusive convection and its implications for the temperature and salinity structure of the ocean and Lake Vanda. J. Phys. Oceanog. 2, 456–4612.0.CO;2>CrossRefGoogle Scholar
Jacobs, C. A. 1978 Numerical simulations of the natural variability in water temperature during BOMEX using alternative forms of the vertical eddy exchange coefficients. J. Phys. Oceanogr. 8, 119–1412.0.CO;2>CrossRefGoogle Scholar
Jacobs, C. A. & Pandolfo, J. P. 1974 A description of a general three-dimensional numerical simulation model of a coupled air-water and/or air-land boundary layer, vol. I. The centre for the Environment and Man, Inc., Rep. no. 4131–509aGoogle Scholar
James, M. L., Smith, G. M. & Wolford, J. C. 1967 Applied Numerical Methods for Digital Computation with FORTRAN. International Textbook, ScrantonGoogle Scholar
Jerlov, N. G. 1966 Optical Oceanography. Amsterdam: ElsevierGoogle Scholar
Katsaros, B. C. 1969 Temperature and salinity of the sea surface with particular emphasis on effects of precipitation. Ph.D. thesis, University of WashingtonGoogle Scholar
Kitaigorodskiy, S. A. 1961 On possibioity of theoretical calculation of vertical temperature profile in upper layer of the sea. Bull. (Izv.) Acad. Sci. U.S.S.R., Geophys. Ser. 3, 313–318Google Scholar
Landis, R. C. 1971 Early BOMEX results of sea surface salinity and Amazon River water. J. Phys. Oceanog. 1, 278–2812.0.CO;2>CrossRefGoogle Scholar
Madsen, O. B. 1977 A realistic model of the wind-induced Ekman boundary layer. J. Phys. Oceanog. 7, 248–2552.0.CO;2>CrossRefGoogle Scholar
Malkus, J. S. 1962 Large-scale interactions. In The Sea (ed. Hill, M. N.), pp. 88–294. New York: InterscienceGoogle Scholar
Mamayev, O. I. 1958 The influence of stratification on vertical turbulent mixing in the sea. Bull. (Izv.) Acad. Sci. U.S.S.R., Geophys. Ser. 7, 870–875Google Scholar
Mazeika, P. A. 1973 Circulation and water masses east of the lesser Antilles. Deut. Hydrografische Zeit. 26, 49–73CrossRefGoogle Scholar
Metcalf, W. G. 1968 Shallow currents along the northeastern coast of South America. J. Mar. Res. 26, 232–243Google Scholar
Miller, J. R. 1976 The salinity effects in a mixed layer ocean model. J. Phys. Oceanog. 6, 29–352.0.CO;2>CrossRefGoogle Scholar
Newman, F. C. 1976 Temperature steps in Lake Kivu: a bottom-heated saline lake. J. Phys. Oceanog. 6, 157–1632.0.CO;2>CrossRefGoogle Scholar
Ostapoff, F. & Worthem, S. 1974 The intradiurnal temperature variation in the upper ocean. J. Phys. Oceanog. 4, 601–6122.0.CO;2>CrossRefGoogle Scholar
Palm, E. 1975 Nonlinear thermal convection. Ann. Rev. Fluid Mech. 7, 39–62CrossRefGoogle Scholar
Pandolfo, J. P. & Jacobs, C. A. 1972 Numerical simulations of the tropical air-sea planetary boundary layer. Boundary-Layer Met. 3, 15–46CrossRefGoogle Scholar
Paulson, C. A., Leavitt, E. & Fleagle, R. G. 1972 Air-sea transfer of momentum, heat, and water determined from profile measurements during BOMEX. J. Phys. Oceanog. 2, 487–4972.0.CO;2>CrossRefGoogle Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
Pierson, W. J. 1964 The interpretation of wave spectrums in terms of the wind profile instead of the wind measured at a constant height. J. Geophys. Res. 24, 5191–6204CrossRefGoogle Scholar
Richtmyer, R. D. & Morton, K. W. 1967 Difference methods for Initial-Value Problems, 2nd edn. New York: InterscienceGoogle Scholar
Ryther, J. H., Menzel, D. W. & Corwin, N. 1967 Influence of the Amazon River outflow on the ecology of the western tropical Atlantic. I. Hydrography and nutrient chemistry. J. Mar. Res. 25, 69–83Google Scholar
Roache, P. J. 1972 Computational Fluid Dynamics. HermosaGoogle Scholar
Sanford, T. E. 1972 Simulation of a one-dimensional model of an undisturbed air-sea boundary layer. Proc. 1972 Summer Computer Simulation Conf., San Diego, pp. 895–902Google Scholar
Shirtcliffe, T. G. L. 1969a An experimental investigation of thermosolutal convection at marginal stability. J. Fluid Mech. 35, 677–688CrossRefGoogle Scholar
Shirtcliffe, T. G. L. 1969b The development of layered thermosolutal convection. Int. J. Heat Mass Transfer 12, 215–222CrossRefGoogle Scholar
Turner, J. S. 1965 The coupled turbulent transports of salt and heat across a sharp density interface. Int. J. Heat Mass Transfer 8, 759–767CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University PressCrossRefGoogle Scholar
Turner, J. S. & Stommel, H. 1964 A new case of convection in the presence of combined vertical salinity and temperature gradients. Proc. U.S. Acad. Sci. 52, 49–53CrossRefGoogle ScholarPubMed
Tyler, J. E. & Preisendorfer, R. W. 1962 Light. In The Sea (ed. Hill, M. N.), pp. 397–451. Wiley-InterscienceGoogle Scholar