• Baringer, M. O., and J. F. Price, 1997a: Mixing and spreading of the Mediterranean outflow. J. Phys. Oceanogr., 27 , 16541677.

  • Baringer, M. O., and J. F. Price, 1997b: Momentum and energy balance of the Mediterranean outflow. J. Phys. Oceanogr., 27 , 16781992.

  • Budillon, G., S. Gremes Cordero, and E. Salusti, 2002: On the dense water spreading off the Ross Sea shelf. J. Mar. Syst., 35 , 207227.

    • Search Google Scholar
    • Export Citation
  • Cushman-Roisin, B., 1994: Introduction to Geophysical Fluid Dynamics. Prentice Hall, 320 pp.

  • England, M. H., and E. Maier-Reimer, 2001: Using chemical tracers to assess ocean models. Rev. Geophys., 39 , 2970.

  • Ertel, H., 1942: Ein neuer hydrodynamischer Wirbelsatz. Meteor. Z., 59 , 277281.

  • Ertel, H., and H. Kuehler, 1949: Ein Theorem ueber die stationaere Wirbelbewegung kompressibler Fluessigkeiten. Z. Angew. Math. Mech., 29 , 109113.

    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Godske, C. L., T. Bergeron, J. Bjerknes, and R. C. Bundgaard, 1957: Dynamic Meteorology and Weather Forecasting. Amer. Meteor. Soc. and Carnegie Inst. Washington, 800 pp.

    • Search Google Scholar
    • Export Citation
  • Haynes, P. H., and M. E. McIntyre, 1987: On the evolution of vorticity and potential vorticity in the presence of diabatic heating and frictional or other forces. J. Atmos. Sci., 44 , 828840.

    • Search Google Scholar
    • Export Citation
  • Haynes, P. H., and M. E. McIntyre, 1990: On the conservation and Impermeability theorems for potential vorticity. J. Atmos. Sci., 47 , 20212031.

    • Search Google Scholar
    • Export Citation
  • Hide, R., 1989: Superhelicity, helicity and potential vorticity. Geophys. Astrophys. Fluid Dyn., 48 , 6979.

  • Hide, R., 1996: Potential magnetic field and potential vorticity in magnetohydrodynamics. Geophys. J. Int., 125 , F. 1F. 3.

  • Jacobsen, J. P., 1930: The mixing of water masses in the sea. Rapp. P.-V. Reun. Comm. Int. Explor. Sci. Mer Mediterr., LXVII. .

  • Kurgansky, M. V., and I. A. Pisnichenko, 2000: Modified Ertel's potential vorticity as a climate variable. J. Atmos. Sci., 57 , 822835.

    • Search Google Scholar
    • Export Citation
  • Luyten, J. R., J. Pedlosky, and H. Stommel, 1983: The ventilated thermocline. J. Phys. Oceanogr., 13 , 292309.

  • Marshall, J., D. Olbers, H. Ross, and D. Wolf-Gladrow, 1993: Potential vorticity constraints on the dynamics and hydrography of the Southern Ocean. J. Phys. Oceanogr., 23 , 465487.

    • Search Google Scholar
    • Export Citation
  • Müller, P., 1995: Ertel potential vorticity theorem in physical oceanography. Rev. Geophys, 33 , 6797.

  • Needler, G. T., 1985: The absolute velocity as a function of conserved measurable quantities. Progress in Oceanography, Vol. 14, Pergamon, 421–429.

    • Search Google Scholar
    • Export Citation
  • Olbers, D. J., M. Wenzel, and J. Willebrand, 1985: The inference of North Atlantic circulation patterns from climatological hydrographic data. Rev. Geophys., 23 , 313356.

    • Search Google Scholar
    • Export Citation
  • Pedlosky, J., 1987: Geophysical Fluid Dynamics. Springer-Verlag, 710 pp.

  • Rhines, P. B., 1986: Vorticity dynamics of the oceanic general circulation. Rev. Fluid Mech., 18 , 433497.

  • Ripa, P., 1981: Symmetries and conservation laws for internal gravity waves. AIP Conf. Proc., 76 , 281306.

  • Roether, W., V. Beitzel, J. Sueltenfuss, and A. Putzka, 1999: The Eastern Mediterranean tritium distribution in 1987. J. Mar. Syst., 20 , 4961.

    • Search Google Scholar
    • Export Citation
  • Salmon, R., 1982: Hamilton's principle and Ertel's theorem. AIP Conf. Proc., 88 , 127135.

  • Salmon, R., 1998: Lectures on Geophysical Fluid Dynamics. Oxford University Press, 378 pp.

  • Salusti, E., and R. Serravall, 1999: On the Ertel and Impermeability theorem for slightly viscous currents with oceanographic applications. Geophys. Astrophys. Fluid Dyn., 90 , 247264.

    • Search Google Scholar
    • Export Citation
  • Stommel, H., and F. Schott, 1977: The beta spiral and the determination of the absolute velocity field from hydrographic station data. Deep-Sea Res., 24 , 325329.

    • Search Google Scholar
    • Export Citation
  • Taylor, G. I., 1931: Internal waves and turbulence in a fluid of variable density. Rapp. P.-V. Reun. Comm. Int. Explor. Sci. Mer Mediterr.,LXXVI, 35–42. [Reprinted, 1960, The Scientific Papers of Sir Geoffrey Ingram Taylor, Vol. II, Cambridge University Press, 240–252.].

    • Search Google Scholar
    • Export Citation
  • Turner, J. S., 1973: Buoyancy Effects in Fluids. Cambridge University Press, 368 pp.

  • Wunsch, C., 1978: The North Atlantic general circulation west of 50° West determined by inverse methods. Rev. Geophys. Space Phys, 16 , 583620.

    • Search Google Scholar
    • Export Citation
  • Wunsch, C., 1996: The Ocean Circulation Inverse Problem. Cambridge University Press, 442 pp.

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

Tracers and Potential Vorticities in Ocean Dynamics

View More View Less
  • 1 Department of Atmospheric and Oceanic Physics, Faculty of Physics and Mathematics, University of Concepción, Concepción, Chile
  • | 2 Institute of Meteorology and Oceanography, University of Naples “Parthenope,” Naples, Italy
  • | 3 INFN, Physics Department, University of Rome “La Sapienza,” Rome, Italy
Restricted access

Abstract

The Ertel potential vorticity theorem for stratified viscous fluids in a rotating system is analyzed herein. A set of “tracers,” that is, materially conserved scalar quantities, and the corresponding Ertel potential vorticities are used to obtain an absolute fluid velocity determination (including both horizontal and vertical components) that generalizes earlier formulations known in the literature within the framework of the beta-spiral method. Potential vorticity fields, respectively, of (i) density, (ii) potential temperature, (iii) salinity, and (iv) the latter's potential vorticities ratio are analyzed in order to infer properties of steady, or quasi-steady, nonhorizontal or slightly viscous currents. For horizontal flows, general conservative properties of a large class of tracer potential vorticities are found and discussed. These ideas are then applied to various steady cases of physical interest, such as density fronts and thermohaline currents. These arguments, together with observational data, are used to obtain some interesting results, even if the values obtained are affected by large experimental errors. Using this method allows the ratio of the vertical and horizontal components of the velocity field to be estimated with greater certainty. Further insight is also gained into a purely hydrological identification of the no-motion level, a classical difficulty in hydrology.

On leave from A. M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia

Corresponding author address: Dr. Ettore Salusti, INFN-Dip. di Fisicà, Universita La Sapienza, Piazzale A. Moro 2, Roma 00185, Italy. Email: ettore.salusti@roma1.infn.it

Abstract

The Ertel potential vorticity theorem for stratified viscous fluids in a rotating system is analyzed herein. A set of “tracers,” that is, materially conserved scalar quantities, and the corresponding Ertel potential vorticities are used to obtain an absolute fluid velocity determination (including both horizontal and vertical components) that generalizes earlier formulations known in the literature within the framework of the beta-spiral method. Potential vorticity fields, respectively, of (i) density, (ii) potential temperature, (iii) salinity, and (iv) the latter's potential vorticities ratio are analyzed in order to infer properties of steady, or quasi-steady, nonhorizontal or slightly viscous currents. For horizontal flows, general conservative properties of a large class of tracer potential vorticities are found and discussed. These ideas are then applied to various steady cases of physical interest, such as density fronts and thermohaline currents. These arguments, together with observational data, are used to obtain some interesting results, even if the values obtained are affected by large experimental errors. Using this method allows the ratio of the vertical and horizontal components of the velocity field to be estimated with greater certainty. Further insight is also gained into a purely hydrological identification of the no-motion level, a classical difficulty in hydrology.

On leave from A. M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, Moscow, Russia

Corresponding author address: Dr. Ettore Salusti, INFN-Dip. di Fisicà, Universita La Sapienza, Piazzale A. Moro 2, Roma 00185, Italy. Email: ettore.salusti@roma1.infn.it

Save