• Batchelor, G. K., 1956: On steady laminar flow with closed streamlines at large Reynolds numbers. J. Fluid Mech.,1, 177–190.

  • Bryan, F. O., 1998: Climate drift in a multicentury integration of the NCAR Climate System Model. J. Climate,11, 1455–1471.

  • Bryan, K., and L. J. Lewis, 1979: A water mass model of the world ocean. J. Geophys. Res.,84, 2503–2517.

  • da Silva, A. M., C. C. Young, and S. Levitus, 1995: Atlas of Surface Marine Data 1994. Vol. 1: Algorithms and Procedures, NOAA Atlas NESDIS 6, 83 pp.

  • de Szoeke, R. A., 1998: The dissipation of fluctuating tracer variances. J. Phys. Oceanogr.,28, 2064–2074.

  • Garrett, C., K. Speer, and E. Tragou, 1995: The relationship between water mass formation and the surface buoyancy flux, with application to Phillips’ Red Sea model. J. Phys. Oceanogr.,25, 1696–1705.

  • Hide, R., 1969: Dynamics of the atmospheres of the major planets with an appendix on the viscous boundary layer at the rigid bounding surface of an electrically-conducting rotating fluid in the presence of a magnetic field. J. Atmos. Sci.,26, 841–853.

  • Joyce, T. M., 1980: On production and dissipation of thermal variance in the oceans. J. Phys. Oceanogr.,10, 460–463.

  • Kalnay, E., and Coauthors, 1996: The NCEP/NCAR 40-Year Reanalysis Project. Bull. Amer. Meteor. Soc.,77, 437–471.

  • Kunze, E., and T. B. Sanford, 1996: Abyssal mixing: Where it is not. J. Phys. Oceanogr.,26, 2286–2296.

  • Ledwell, J. R., A. J. Watson, and C. S. Law, 1993: Evidence for slow mixing across the pycnocline from an open-ocean tracer-release experiment. Nature,364, 701–703.

  • Levitus, S., 1982: Climatological Atlas of the World Ocean. NOAA Prof. Paper No. 13. U.S. Dept. of Commerce, 173 pp.

  • Manabe, S., K. Bryan, and M. J. Spelman, 1990: Transient response of a global ocean–atmosphere model to a doubling of atmospheric carbon dioxide. J. Phys. Oceanogr.,20, 722–749.

  • Munk, W. H., 1966: Abyssal recipes. Deep-Sea Res.,13, 707–730.

  • Niiler, P., and J. Stevenson, 1982: The heat budget of tropical ocean warm-water pools. J. Mar. Res.,40 (Suppl.), 465–480.

  • Oberhuber, J. M., 1988: An atlas based on the ‘COADS’ data set: The budgets of heat, buoyancy and turbulent kinetic energy at the surface of the global ocean. Max-Planck-Institut für Meteorologie, Hamburg, Rep. 15, 199 pp.

  • Pacanowski, R. C., 1996: MOM 2 version 2.0 (beta) documentation user’s guide and reference manual. GFDL Ocean Tech. Rep. 3.2. [Available from GFDL/NOAA, Princeton University, Princeton, NJ 08542].

  • Pedlosky, J., 1996: Ocean Circulation Theory. Springer Verlag, 453 pp.

  • Rooth, C. G., and H. G. Östlund, 1972: Penetration of tritium into the Atlantic thermocline. Deep-Sea Res.,19, 481–492.

  • Schneider, E. K., 1977: Axially symmetric steady state models of the basic state for instability and climate studies. Part II: Nonlinear calculations. J. Atmos. Sci.,34, 280–292.

  • Speer, K. G., 1997: A note on average cross-isopycnal mixing in the North Atlantic ocean. Deep-Sea Res.,44, 1981–1990.

  • Stern, M. E., 1975: Ocean Circulation Physics. Academic, 246 pp.

  • Toole, J. M., K. L. Polzin, and R. W. Schmitt, 1994: Estimates of diapycnal mixing in the abyssal ocean. Science,264, 1120–1123.

  • Walin, G., 1982: On the relation between sea-surface heat flow and thermal circulation in the ocean. Tellus,34, 187–195.

  • Zhang, H.-M., and L. D. Talley, 1998: Heat and buoyancy budgets and mixing rates in the upper thermocline of the Indian and global oceans. J. Phys. Oceanogr.,28, 1961–1978.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 0 0 0
PDF Downloads 0 0 0

A Dissipation Integral with Application to Ocean Diffusivities and Structure

View More View Less
  • 1 Center for Ocean–Land–Atmosphere Studies, Calverton, Maryland
Restricted access

Abstract

An integral balance is developed for steady fluid flows relating dissipation in volumes bounded by isosurfaces of a tracer (quasi-conserved quantity) and solid boundaries to the covariance of the tracer value and surface fluxes across the boundaries. The balance is used to estimate upper bounds for vertical eddy diffusion coefficients for temperature and salinity in various volumes of the ocean. The vertical temperature diffusivity is calculated to be small, O(0.1 × 10−4 m2 s−1), except for the warmest and coldest volumes of the ocean. The vertical salinity diffusivity for the volume that makes up most of the deep ocean is estimated to be O(1 × 10−4 m2 s−1). Sources of error in these calculations are discussed, and the sensitivity to errors in the surface flux data is evaluated.

The dissipation integral is also applied to demonstrate some related results concerning extrema and homogenization. The Prandtl–Batchelor theorem is a special case of one of these results. As a consequence of these results, if turbulent transfer is downgradient and there are no internal sources or sinks, a necessary (but not sufficient) condition for a climatological tracer distribution to be in a steady state is the absence of internal extrema. The climatological salinity distribution does not appear to violate this condition.

Corresponding author address: Edwin K. Schneider, Center for Ocean–Land–Atmosphere Studies, 4041 Powder Mill Rd., Suite 302, Calverton, MD 20705-3106.

Email: schneide@cola.iges.org

Abstract

An integral balance is developed for steady fluid flows relating dissipation in volumes bounded by isosurfaces of a tracer (quasi-conserved quantity) and solid boundaries to the covariance of the tracer value and surface fluxes across the boundaries. The balance is used to estimate upper bounds for vertical eddy diffusion coefficients for temperature and salinity in various volumes of the ocean. The vertical temperature diffusivity is calculated to be small, O(0.1 × 10−4 m2 s−1), except for the warmest and coldest volumes of the ocean. The vertical salinity diffusivity for the volume that makes up most of the deep ocean is estimated to be O(1 × 10−4 m2 s−1). Sources of error in these calculations are discussed, and the sensitivity to errors in the surface flux data is evaluated.

The dissipation integral is also applied to demonstrate some related results concerning extrema and homogenization. The Prandtl–Batchelor theorem is a special case of one of these results. As a consequence of these results, if turbulent transfer is downgradient and there are no internal sources or sinks, a necessary (but not sufficient) condition for a climatological tracer distribution to be in a steady state is the absence of internal extrema. The climatological salinity distribution does not appear to violate this condition.

Corresponding author address: Edwin K. Schneider, Center for Ocean–Land–Atmosphere Studies, 4041 Powder Mill Rd., Suite 302, Calverton, MD 20705-3106.

Email: schneide@cola.iges.org

Save