Stability of the thermohaline circulation examined with a one-dimensional fluid loop

References

• de Boer, A. M., Gnanadesikan, A., Edwards, N. R. and Watson, A. J. 2010. Meridional density gradients do not control the atlantic overturning circulation. J. Phys. Oceanogr. 40(2), 368–380. DOI: 10.1175/2009JPO4200.1.
   Web of Science ®Google Scholar
• Dewar, W. K. and Huang, R. X. 1996. On the forced flow of salty water in a loop. Phys. Fluids 8, 954–970. DOI: 10.1063/1.868874.
   Web of Science ®Google Scholar
• Dijkstra, H. A. 2005. Nonlinear physical oceanography: a dynamical systems approach to the large scale ocean circulation and El Nino, Vol. 28, Springer Science, New York, 523 pp.
   Google Scholar
• Dijkstra, H. A. and Weijer, W. 2005. Stability of the global ocean circulation: Basic bifurcation diagrams. J. Phys. Oceanogr. 35(6), 933–948. DOI: 10.1175/JPO2726.1.
   Web of Science ®Google Scholar
• Gnanadesikan, A. 1999. A simple predictive model for the structure of the oceanic pycnocline. Science 283(5410), 2077–2079.
   PubMed Web of Science ®Google Scholar
• Gregory, J. M., Saenko, O. A. and Weaver, A. J. 2003. The role of the atlantic freshwater balance in the hysteresis of the meridional overturning circulation. Climate Dyn. 21(7), 707–717. DOI: 10.1007/s00382-003-0359-8.
   Web of Science ®Google Scholar
• Hawkins, E., Smith, R. S., Allison, L. C., Gregory, J. M., Woollings, T. J., and co-authors. 2011. Bistability of the atlantic overturning circulation in a global climate model and links to ocean freshwater transport. Geophys. Res. Lett. 38(10), DOI: 10.1029/2011GL047208.
   Web of Science ®Google Scholar
• Hazewinkel, J., Paparella, F. and Young, W. R. 2012. Stressed horizontal convection. J. Fluid Mech. 692, 317–331. DOI: 10.1017/jfm.2011.514.
   Web of Science ®Google Scholar
• Held, I. M. 2005. The gap between simulation and understanding in climate modeling. Bull. Am. Meteorol. Soc. 86(11), 1609–1614. DOI: 10.1175/BAMS-86-11-1609.
   Web of Science ®Google Scholar
• Huang, R. X. 1999. Mixing and energetics of the oceanic thermohaline circulation. J. Phys. Oceanogr. 29(4), 727–746. DOI: 10.1175/1520-0485(1999)029\lt0727:MAEOTO\gt2.0.CO;2.
   Web of Science ®Google Scholar
• Keller, J. B. 1966. Periodic oscillations in a model of thermal convection. J. Fluid Mech. 26(3), 599–606. DOI: 10.1017/S0022112066001423.
   Web of Science ®Google Scholar
• Malkus, W. V. 1972. Non-periodic convection at high and low prandtl number. Mem. Soc. R. Sci. Liege 4(6), 125–128.
   Google Scholar
• Marotzke, J. 2000. Abrupt climate change and thermohaline circulation: Mechanisms and predictability. Proc. Nat. Acad. Sci. 97(4), 1347–1350.
   Web of Science ®Google Scholar
• Marshall, J., Donohoe, A., Ferreira, D. and McGee, D. 2013. The ocean’s role in setting the mean position of the inter-tropical convergence zone. Climate Dyn. 42(7), 1967–1979. DOI: 10.1007/s00382-013-1767-z.
   Web of Science ®Google Scholar
• Nilsson, J. and Walin, G. 2001. Freshwater forcing as a booster of thermohaline circulation. Tellus A 53(5), 629–641. DOI: 10.1034/j.1600-0870.2001.00263.x.
   Google Scholar
• Park, Y.-G. and Bryan, K. 2000. Comparison of thermally driven circulations from a depth-coordinate model and an isopycnal-layer model. Part i: Scaling-law sensitivity to vertical diffusivity. J. Phys. Oceanogr. 30(3), 590–605. DOI: 10.1175/1520-0485(2000)030\lt0590:COTDCF\gt2.0.CO;2.
   Web of Science ®Google Scholar
• Pollmann, F., Roquet, F. and Madec, G. 2015. Effects of the asymmetry between surface and interior flow on the dynamics of a thermohaline loop. J. Phys. Oceanogr. 45, 2544–2563. DOI: 10.1175/JPO-D-15-0022.1.
   Web of Science ®Google Scholar
• Rahmstorf, S. 2002. Ocean circulation and climate during the past 120,000 years. Nature 419(6903), 207–214. DOI: 10.1038/nature01090.
   Web of Science ®Google Scholar
• Rahmstorf, S., Crucifix, M., Ganopolski, A., Goosse, H., Kamenkovich, I, and co-authors. 2005. Thermohaline circulation hysteresis: a model intercomparison. Geophys. Res. Lett. 32(23), DOI: 10.1029/2005GL023655.
   Web of Science ®Google Scholar
• Rooth, C. 1982. Hydrology and ocean circulation. Prog. Oceanogr. 11(2), 131–149. DOI: 10.1016/0079-6611(82)90006-4.
   Web of Science ®Google Scholar
• Roquet, F., Madec, G., Brodeau, L. and Nycander, J. 2015a. Defining a simplified yet ‘realistic’ equation of state for seawater. J. Phys. Oceanogr. 45, 2564–2579. DOI: 10.1175/JPO-D-15-0080.1.
   Web of Science ®Google Scholar
• Roquet, F., Madec, G., McDougall, T. J. and Barker, P. M. 2015. Accurate polynomial expressions for the density and specific volume of seawater using the teos-10 standard. Ocean Model. 90, 29–43. DOI: 10.1016/j.ocemod.2015.04.002.
   Web of Science ®Google Scholar
• Ruddick, B. and Zhang, L. 1996. Qualitative behavior and nonoscillation of stommel’s thermohaline box model. J. Climate 9(11), 2768–2777. DOI: 10.1175/1520-0442(1996)009\lt2768:QBANOS\gt2.0.CO;2.
   Web of Science ®Google Scholar
• Sévellec, F., Huck, T. and Ben Jelloul, M. 2006. On the mechanism of centennial thermohaline oscillations. J. Marine Res. 64(3), 355–392. DOI: 10.1357/002224006778189608.
   Web of Science ®Google Scholar
• Stommel, H. 1961. Thermohaline convection with two stable regimes of flow. Tellus 13(2), 224–230. DOI: 10.1111/j.2153-3490.1961.tb00079.x.
   Google Scholar
• Stouffer, R. J., Yin, J., Gregory, J. M., Dixon, K. W., Spelman, M. J. and co-authors. 2006. Investigating the causes of the response of the thermohaline circulation to past and future climate changes. J. Climate 19(8), 1365–1387. DOI: 10.1175/JCLI3689.1.
   Web of Science ®Google Scholar
• Tziperman, E., Toggweiler, J. R., Bryan, K. and Feliks, Y. 1994. Instability of the thermohaline circulation with respect to mixed boundary conditions: is it really a problem for realistic models? J. Phys. Oceanogr. 24(2), 217–232. DOI: 10.1175/1520-0485(1994)024\lt0217:IOTTCW\gt2.0.CO;2.
   Web of Science ®Google Scholar
• Vellinga, M. and Wood, R. A. 2002. Global climatic impacts of a collapse of the atlantic thermohaline circulation. Climatic Change 54(3), 251–267. DOI: 10.1023/A:1016168827653.
   Web of Science ®Google Scholar
• Welander, P. 1967. On the oscillatory instability of a differentially heated fluid loop. J. Fluid Mech. 29, 17–30.
   Web of Science ®Google Scholar
• Welander, P. 1982. A simple heat-salt oscillator. Dyn. Atmos. Oceans 6(4), 233–242. DOI: 10.1016/0377-0265(82)90030-6.
   Web of Science ®Google Scholar
• Welander, P. 1986. Thermohaline effects in the ocean circulation and related simple models. In: Large-Scale Transport Processes in Oceans and Atmosphere (eds. J. Willebrand and D. L. T. Anderson). D. Reidel, Hingham, Mass. pp. 163–200. DOI: 10.1007/978-94-009-4768-9\_4.
   Google Scholar
• Wunsch, C. 2005. Thermohaline loops, stommel box models, and the sandström theorem. Tellus A 57(1), 84–99. DOI: 10.1111/j.1600-0870.2005.00093.x.
   Google Scholar
• Wunsch, C. and Ferrari, R. 2004. Vertical mixing energy and the general circulation of the oceans. Ann. Rev. Fluid Mech. 36, 281–314. DOI: 10.1146/annurev.fluid.36.050802.122121.
   Web of Science ®Google Scholar
• Wunsch, C. and Heimbach, P. 2013. Two decades of the atlantic meridional overturning circulation: Anatomy, variations, extremes, prediction, and overcoming its limitations. J. Climate 26, 7167–7186. DOI: 10.1175/JCLI-D-12-00478.1.
   Web of Science ®Google Scholar
• Yin, J., Schlesinger, M. E., Andronova, N. G., Malyshev, S. and Li, B. 2006. Is a shutdown of the thermohaline circulation irreversible? J. Geophys. Res. Atmos. 111(D12). DOI: 10.1029/2005JD006562, d12104.
   Web of Science ®Google Scholar
• Young, W. R. 2010. Dynamic enthalpy, conservative temperature, and the seawater Boussinesq approximation. J. Phys. Oceanogr. 40, 394–400.
   Web of Science ®Google Scholar
• Yuan, S. and Wunsch, C. 2005. Stress-driven thermohaline loops. Phys. Fluids (1994-present) 17(6), 066601. DOI: 10.1063/1.1927887.
   Web of Science ®Google Scholar