Ocean Science www.ocean-sci.net 1812-0784 1812-0792 3 1 2007 10.5194/os-3-17-2007 http://www.ocean-sci.net/3/17/2007/ http://www.ocean-sci.net/3/17/2007/os-3-17-2007.html http://www.ocean-sci.net/3/17/2007/os-3-17-2007.pdf 17 30 2007-01-26 Overturning cells in the Southern Ocean and subtropical gyres J. A. Polton jpolton@ucsd.edu D. P. Marshall Department of Meteorology, University of Reading, UK The circulation of the subtropical gyres can be decomposed into a horizontal recirculation along contours of constant Bernoulli potential and an overturning circulation across these contours. While the geometry and topology of Bernoulli contours is more complicated in the subtropical gyres than in the Southern Ocean, these subtropical overturning circulations are very much analogous to the overturning cell found in the Southern Ocean. This analogy is formalised through an exact integral constraint, including the rectified effects of transient eddies. The constraint can be interpreted either in terms of vertical fluxes of potential vorticity, or equivalently as an integral buoyancy budget for an imaginary fluid parcel recirculating around a closed Bernoulli contour. Under conditions of vanishing buoyancy and mechanical forcing, the constraint reduces to a generalised non-acceleration condition, under which the Eulerian-mean and eddy-induced overturning circulations exactly compensate. The terms in the integral constraint are diagnosed in an eddy-permitting ocean model in both the North Pacific subtropical gyre and the Southern Ocean. The extent to which the Eulerian-mean and eddy-induced overturning circulations compensate is discussed in each case. Cessi, P. and Fantini, M.: The eddy-driven thermocline, J. Phys. Oceanogr., 34, 2642–2658, 2004. Danabasoglu, G., McWilliams, J C., and Gent, P R.: The Role of Mesoscale Tracer Transports in the Global Ocean Circulation, Science, 264, 1123–1126, 1994. Döös, K. and Webb, D J.: The Deacon Cell and the Other Meridional Cells of the Southern Ocean, J. Phys. Oceanogr., 24, 429–442, 1994. Drijfhout, S S.: What Sets the Surface Eddy Mass Flux in the Southern Ocean?, J. Phys. Oceanogr., 35, 2152–2166, 2005. Eliassen, A. and Palm, E.: On the transfer of energy in stationary mountain waves, Geofys. Publ., 22, 1–23, 1961. Gallego, B., Cessi, P., and McWilliams, J C.: The Antarctic Circumpolar Current in Equilibrium, J. Phys. Oceanogr., 34, 1571–1587, 2004. Gent, P R., Willebrand, J., McDougall, T J., and McWilliams, J C.: Parameterizing eddy-induced tracer transports in ocean circulation models, J. Phys. Oceanogr., 25, 463–474, 1995. Gille, S T.: The Southern Ocean Momentum Balance: Evidence for Topographic Effects from Numerical Model Output and Altimeter Data, J. Phys. Oceanogr., 27, 2219–2232, 1997. Haynes, P H. and McIntyre, M E.: On the Evolution of Vorticity and Potential Vorticity in the Presence of Diabatic Heating and Frictional or Other Forces, J. Atmos. Sci., 44, 828–841, 1987. Haynes, P H. and McIntyre, M E.: On the Conservation and Impermeability Theorems for Potential Vorticity, J. Atmos. Sci., 47, 2021–2031, 1990. Henning, C C. and Vallis, G K.: The Effects of Mesoscale Eddies on the Main Subtropical Thermocline, J. Phys. Oceanogr., 34, 2428–2443, 2004. Hughes, C W., Jones, M S., and Carnochan, S A.: Use of transient features to identify eastward currents in the Southern Ocean, J. Geophys. Res., 103, 2929–2944, 1998. Johnson, G C. and Bryden, H L.: On the size of the Antarctic Circumpolar Current, Deep-Sea Res., 36, 39–53, 1989. Karsten, R., Jones, H., and Marshall, J.: The role of eddy transfer in setting the stratification and transport of a Circumpolar Current, J. Phys. Oceanogr., 32, 39–54, 2002. Karsten, R H. and Marshall, J.: Constructing the residual circulation of the ACC from observations, J. Phys. Oceanogr., 32, 3315–3327, 2002. Luyten, J R., Pedlosky, J., and Stommel, H.: The Ventilated Thermocline, J. Phys. Oceanogr., 13, 292–309, 1983. Marshall, D P.: Subduction of water masses in an eddying ocean, J. Mar. Res., 55, 201–222, 1997. Marshall, D P.: Vertical Fluxes of Potential Vorticity and the Structure of the Thermocline, J. Phys. Oceanogr., 30, 3102–3112, 2000. Marshall, D P., Williams, R G., and Lee, M.-M.: The relation between eddy-induced transport and isopycnic gradients of potential vorticity, J. Phys. Oceanogr., 29, 1571–1578, 1999. McDougall, T J.: Neutral Surfaces, J. Phys. Oceanogr., 17, 1950–1964, 1987. Marshall, J., Jones, H., Karsten, R., and Wardle, R.: Can eddies set ocean stratification?, J. Phys. Oceanogr., 32, 26–38, 2002. Obukhov, A M.: On the dynamics of a stratified liquid, Dokl. Akad. Nauk SSSR, 145, 1239–1242, (English: 1963, Sov. Phys. Dolk., 7(8), 682–684), 1962. Olbers, D.: Comments on "On the Obscurantist Physics of "Form Drag" in Theorizing about the Circumpolar Current", J. Phys. Oceanogr., 28, 1647–1654, 1998. Olbers, D., Borowski, D., Völker, C., and Wölff, J.-O.: The dynamical balance, transport and circulation of the Antarctic Circumpolar Current, Antarctic Science, 16, 439–470, 2004. Plumb, R A.: A Nonacceleration Theorem for Transient Quasi-geostrophic Eddies on a Three-Dimensional Time-Mean Flow, J. Atmos. Sci., 47, 1825–1836, 1990. Polton, J A. and Marshall, D P.: Understanding the structure of the subtropical thermocline, J. Phys. Oceanogr., 33, 1240–1249, 2003. Radko, T. and Marshall, J.: The Leaky Thermocline, J. Phys. Oceanogr., 34, 1648–1662, 2004. Rintoul, S R., Hughes, C W., and Olbers, D.: Ocean Circulation and Climate: Observing and modelling the global ocean, chap. 4.6, Acedemic Press, 2001. Roberts, M J. and Marshall, D P.: On the Validity of downgradient eddy closures in ocean models, J. Geophys. Res., 105, 28 613–28 627, 2000. Salmon, R.: The Thermocline as an "internal boundary layer", J. Mar. Res., 48, 437–469, 1990. Schmitz, W J.: On the World Ocean Circulation: Volume II. The Pacific and Indian Oceans / A global update, Woods Hole Oceanog. Inst. Tech. Rept., WHOI-96-08, pp245, 1996. Speer, K., Rintoul, S R., and Sloyan, B.: The Diabatic Deacon Cell, J. Phys. Oceanogr., 30, 3212–3222, 2000. Stevens, D P. and Ivchenko, V O.: The Zonal Momentum Balance in an Eddy Resolving General Circulation Model of the Southern Ocean, Quart. J. Roy. Meteor. Soc., 123, 929–951, 1997. Treguier, A M., Held, I M., and Larichev, V D.: Parameterization of Quasigeostrophic Eddies in Primitive Equation Ocean Models, J. Phys. Oceanogr., 27, 567–580, 1997. Truesdell, C.: Proof that Ertel's vorticity theorem holds in average for any medium suffering no tangential acceleration on the boundary, Geofis. Pura Appl., 19, 167–169, 1951. Webb, D J., de~Cuevas, B A., and Coward, A C.: The first main run of the OCCAM global ocean model, Tech. rep., SOC Internal document No. 34, James Rennell Division, Southampton Oceanography Centre, S014 3ZH, UK, 43 pp, 1998. White, A A. and Bromley, R A.: Dynamically consistent, quasi-hydrostatoc equations for global models with a complete representation of the Coriolis force, Q. J. R. Meteorol. Soc., 121, 399–418, 1995.