Thermohaline loops, Stommel box models, and the Sandström theorem

Carl Wunsch

doi:10.3402/tellusa.v57i1.14607

Thermohaline loops, Stommel box models, and the Sandström theorem

Tellus

Volume 57 (2005): Issue 1

By: Carl Wunsch

Open Access

|Jan 2005

Adcroft , A. , Scott , J. R. and Marotzke , J. 2001 . Impact of geothermal heating on the global ocean circulation . Geophys. Res. Lett . 28 , 1735 – 1738 .
Search in Google Scholar Back to article
Cessi , P. and Young , W. R. 1992 . Multiple equilibria in two-dimensional thermohaline circulation . J. Fluid Mech . 241 , 291 – 309 .
Search in Google Scholar Back to article
Colin de Verdière , A. 1993 . On the oceanic thermohaline circulation. In: Modelling Oceanic Climate Intereactions (eds J. Willebrand , and D. L. T. Anderson ). Springer-Verlag , Berlin , 151 - 184 .
Search in Google Scholar Back to article
Creveling , H. F. , de Paz , J. E , Baladi J. Y. and Schoenhals , R. J. 1975 . Stability characteristics of a single-phase free convection loop . J. Fluid Mech . 67 , 65 – 84 .
Search in Google Scholar Back to article
Defant , A. 1961 . Physical Oceanography , Vol. 1 . Pergamon , New York , 598 pp.
Search in Google Scholar Back to article
Dewar , W. K. and Huang , R. X. 1995 . On the forced flow of salty water in a loop . Phys. Fluids 8 , 954 – 970 .
Search in Google Scholar Back to article
Dijkstra , H. A. and Weijer , W. 2003 . The connection of equilibria within a hierarchy of models . J. Mar Res . 61 , 725 – 744 .
Search in Google Scholar Back to article
Erhard , P. and Müller , U. 1990 . Dynamical behavior of natural convec-tion in a single-phase loop . J. Fluid Mech . 217 , 487 – 518 .
Search in Google Scholar Back to article
Hart , J. E. 1984 . A new analysis of the closed loop thermosyphon . Int. J. Heat Mass Transf 27 , 125 – 136 .
Search in Google Scholar Back to article
Huang , R. X. 1993 . Real freshwater flux as a natural boundary condi-tion for the salinity balance and thermohaline circulation forced by evaporation and precipitation . J. Phys. Oceanogr 23 , 2428 – 2446 .
Search in Google Scholar Back to article
Huang , R. X. 1999 . Mixing and energetics of the oceanic thermohaline circulation . J. Phys. Oceanogr 29 , 727 – 746 .
Search in Google Scholar Back to article
Huang , R. X. and Dewar , W. K. 1996 . Haline circulation: bifurcation and chaos . J. Phys. Oceanogr . 26 , 2093 – 2106 .
Search in Google Scholar Back to article
Jayne , S. R. and St. Laurent , L. C. 2001 . Parametrizing tidal dissipation over rough topography . Geophys. Res. Lett . 28 , 811 – 814 .
Search in Google Scholar Back to article
Jeffreys , H. W. 1925 . On fluid motions produced by differences of tem-perature and humidity . Q. J. R. Meteorol. Soc . 51 , 347 – 356 .
Search in Google Scholar Back to article
Jiang , Y. Y. and Shoji , M. 2003 . Spatial and temporal instabilities of in a natural circulation loop: influences of thermal boundary conditions . J. Heat Transfer; Trans. ASME 125 , 612 – 623 .
Search in Google Scholar Back to article
Keller , J. B. 1966 . Periodic oscillations in a model of thermal convection . J. Fluid Mech . 26 , 599 – 606 .
Search in Google Scholar Back to article
Kundu , P. K. 1990 . Fluid Mechanics . Academic , San Diego , 638 pp.
Search in Google Scholar Back to article
Lorenz , E. N. 1963 . Deterministic non-periodic flow . J. Atmos. Sci . 20 , 130 – 141 .
Search in Google Scholar Back to article
Lorenz , E. N. 1990 . Can chaos and intransitivity lead to interannual variability? Tellus 42A , 378 – 389 .
Search in Google Scholar Back to article
Maas , L. R. M., 1994 . A simple model for the three-dimensional, thermally and wind-driven ocean circulation . Tellus 46A , 671 – 680 .
Search in Google Scholar Back to article
McDougall , T. J. and Dewar , W. K. 1998 . Vertical mixing and cabbeling in layered models . J. Phys. Oceanogr 28 , 1458 – 1480 .
Search in Google Scholar Back to article
Malkus , W. V. R. 1972 . Non-periodic convection at high and low Prandtl number. Mém. Soc. Royale des Sciences de Liège, 6th serie, tome IV, 125 - 128 .
Search in Google Scholar Back to article
Manabe , S. and Stouffer , R. J. 1999 . Are two modes of thermohaline circulation stable? Tellus 51A , 400 – 411 .
Search in Google Scholar Back to article
Marotzke , J. 2000 . Abrupt climate change and thermohaline circulation: Mechanisms and predictability . Proc. Natl. Acad. US . 97 , 1347 – 1350 .
Search in Google Scholar Back to article
Mertol , A. , Greif , R. and Zvirin , Y. 1981 . The transient, steady state and stability behavior of a thermosyphon with throughflow . Int. J. Mass Heat Transfer 24 , 621 – 633 .
Search in Google Scholar Back to article
Munk , W. and Wunsch , C. 1998 . Abyssal recipes II: energetics of tidal and wind mixing . Deep-Sea Res . 45 , 1976 – 2009 .
Search in Google Scholar Back to article
Nilsson , J. and Walin , G. 2001 . Freshwater forcing as a booster of ther-mohaline circulation . Tellus 53A , 629 – 641 .
Search in Google Scholar Back to article
Nilsson , J. , Broström , G. and Walin , G. 2003 . The thermohaline cir-culation and vertical mixing: does weaker density stratification give stronger overturning? J. Phys. Oceanogr 33 , 2781 – 2795 .
Search in Google Scholar Back to article
Oberhuber , J. M. 1993 . Simulation of the Atlantic circulation with a coupled sea ice-mixed layer isopycnal general circulation model. Part I: model description . J. Phys. Oceanogr 23 , 808 – 829 .
Search in Google Scholar Back to article
Palmer , T. N. 1999 . A nonlinear dynamical perspective on climate pre-diction . J. Climate 12 , 575 – 591 .
Search in Google Scholar Back to article
Paparella , E and Young , W. R. 2002 . Horizontal convection is non-turbulent . J. Fluid Mech . 466 , 205 – 214 .
Search in Google Scholar Back to article
Pasquero , C. and Tziperman , E. 2004 . Effects of a wind-driven gyre on themohaline circulation variability . J. Phys. Oceanogr 34 , 805 – 816 .
Search in Google Scholar Back to article
Pedlosky , J. 1996 . Ocean Circulation Theory . Springer-Verlag , Berlin , 450 pp.
Search in Google Scholar Back to article
Sandström , J. W. 1908 . Dynamicsche Versuche mit Meerwasser . Annalen der Hydrographie under Martimen Meteorologie 36 , 6 – 23 .
Search in Google Scholar Back to article
Stern , M. E. 1975 . Ocean Circulation Physics . Academic , New York , 246 pp.
Search in Google Scholar Back to article
Stommel , H. 1961 . Thermohaline convection with two stable regimes of flow . Tellus 13 , 131–149 ( S61 ).
Search in Google Scholar Back to article
Stommel , H. and Rooth , C. 1968 . On the interaction of gravitational and dynamic forcing in simple circulation models . Deep-Sea Res . 15 , 165 – 170 .
Search in Google Scholar Back to article
Thual , O. and McWilliams , J. C. 1992 . The catastrophe structure of themohaline convection in a two-dimensional fluid model and a com-parison with low-order box models . Geophys. Astrophys. Fluid Dyn . 64 , 67 – 95 .
Search in Google Scholar Back to article
Tritton , D. J. 1988 . Physical Fluid Dynamics . 2nd edn , Oxford Univ. Press , Oxford , 519 pp.
Search in Google Scholar Back to article
Tziperman , E. , Toggweiler , J. R. , Felilcs , Y. and Bryan , K. 1994 . Insta-bility of the thermohaline circulation with respect to mixed boundary-conditions-is it really a problem for realistic models? J. Phys. Oceanogr . 24 , 217 – 232 .
Search in Google Scholar Back to article
Wang , Y. , Singer , J. and Bau , H. U. 1992 . Controlling chaos in a thermal convection loop . J. Fluid Mech . 237 , 479 – 498 .
Search in Google Scholar Back to article
Welander , P. 1967 . On the oscillatory instability of a differentially heated fluid loop . J. Fluid Mech . 29 , 17 – 30 .
Search in Google Scholar Back to article
Welander , P. 1985 . Thermohaline effects in the ocean circulation and related simple models. In: Large-Scale Transport Processes in Oceans and Atmosphere, NATO ASI Series C . Vol . 190 , 163 – 200 .
Search in Google Scholar Back to article
Whitehead , J. A. 1995 . Thermohaline ocean processes and models . Ann. Rev. Fluid Mech . 27 , 89 – 113 .
Search in Google Scholar Back to article
Wright , D. G. , Stocker , T. E and Mercer , D. 1998 . Closures used in zonally averaged models . J. Phys. Oceanogr , 28 , 791 – 804 .
Search in Google Scholar Back to article
Wunsch , C. 2002 . What is the thermohaline circulation? Science 298 , 1180 – 1181 .
Search in Google Scholar Back to article
Wunsch , C. and Ferrari , R. 2004 . Vertical mixing, energy, and the general circulation of the oceans. Ann. Revs. Fl. Mech . 36 , doi: 10.1146/annurev.fluid.36.050802.122121 .
Open DOI Search in Google Scholar Back to article
Wunsch , C. 2005 . Speculations on a schematic Theory of The Younger Dryas. J. Mor. Res . 63 ( Fofonoff Vol.), in press .
Search in Google Scholar Back to article