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Rotating horizontal convection and the potential vorticity constraint

Published online by Cambridge University Press:  16 August 2016

Yu Zhang ,
Chen Chen ,
Zhengguang Zhang  and
Wei Wang
Yu Zhang*
Affiliation:
Physical Oceanography Laboratory/CIMST, Ocean University of China and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China
Chen Chen
Affiliation:
Lamont-Doherty Earth Observatory, Columbia University, Palisades, NY 10964, USA
Zhengguang Zhang
Affiliation:
Physical Oceanography Laboratory/CIMST, Ocean University of China and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China
Wei Wang
Affiliation:
Physical Oceanography Laboratory/CIMST, Ocean University of China and Qingdao National Laboratory for Marine Science and Technology, Qingdao, China
*
†Email address for correspondence: yuz@ouc.edu.cn
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Abstract

Horizontal convection, with a focus on the essential physics it can disclose for the oceanic overturning circulation, is studied in an annular gap where differential heating is applied along the bottom. Based on the three-dimensional distribution of both velocity and temperature fields, we propose that in addition to differential buoyancy forcing and diapycnal mixing, potential vorticity (PV) can also be a limiting factor for the overturning circulation by imposing a constraint on the meridional flow. With rotation, flow has to be along PV contours excepting that effects of diffusion or friction exist to break the PV constraint. In the axisymmetric rotating experiment, the flow along isotherms is to zero-order azimuthal, due to the fact that PV varies only along the radial direction. Consequently, the radial flow appears at the next order with much smaller amplitude, leading to a much weaker overturning circulation compared with that of the non-rotating experiment. In the presence of a full radial barrier, the annular gap can be viewed as a four-sided domain with its northern boundary along the inner cylinder, and the meridional flow shows remarkable inhomogeneity in space. In the absence of any background PV gradient, the flow field equilibrates itself to a state where the PV contours above the bottom boundary layer are largely radial, particularly in a sub-region near the western boundary, allowing a relatively strong radial geostrophic flow and greatly strengthening the overturning circulation from the case without the barrier.

JFM classification

Convection: Convection Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Rotating flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 803 , 25 September 2016 , pp. 72 - 93
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Copyright
© 2016 Cambridge University Press 

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References

Barkan, R., Winters, K. B. & Smith, S. G. L. 2013 Rotating horizontal convection. J. Fluid Mech. 723, 556–586.CrossRefGoogle Scholar
Beardsley, R. C. & Festa, J. F. 1972 A numerical model of convection driven by a surface stress and non-uniform horizontal heating. J. Phys. Oceanogr. 2, 444–455.Google Scholar
Chiu-Webster, S., Hinch, E. J. & Lister, J. 2008 Very viscous horizontal convection. J. Fluid Mech. 611, 395–426.CrossRefGoogle Scholar
Coman, M. A., Griffiths, R. W. & Hughes, G. O. 2006 Sandström’s experiments revisited. J. Mar. Res. 64, 783–796.Google Scholar
Gayen, B., Griffiths, R. W. & Hughes, G. O. 2014 Stability transition and turbulence in horizontal convection. J. Fluid Mech. 751, 698–724.Google Scholar
Hignett, P., Ibbetson, A. & Killworth, P. D. 1981 On rotating thermal convection driven by non-uniform heating from below. J. Fluid Mech. 109, 161–187.Google Scholar
Hogg, N. G. 1983 A note on the deep circulation of the western north atlantic: its nature and causes. Deep-Sea Res. 30, 945–961.Google Scholar
Hughes, G. O. & Griffiths, R. W. 2008 Horizontal convection. Annu. Rev. Fluid Mech. 40, 185–208.Google Scholar
Hussam, W. K., Tsai, T. K. & Sheard, G. J. 2014 The effect of rotation on radial horizontal convection and Nusselt number scaling in a cylindrical container. Intl J. Heat Mass Transfer 77, 46–59.Google Scholar
Ilicak, M. & Vallis, G. K. 2012 Simulations and scaling of horizontal convection. Tellus A 64, 118377.Google Scholar
Jeffreys, H. 1925 On fluid motions produced by differences of temperature and humidity. Q. J. R. Meteorol. Soc. 51, 347–356.Google Scholar
Lumpkin, R. & Speer, K. 2007 Global ocean meridional overturning. J. Phys. Oceanogr. 37, 2550–2562.Google Scholar
Luyten, J. R., Pedlosky, J. & Stommel, H. 1983 The ventilated thermocline. J. Phys. Oceanogr. 13, 292–309.Google Scholar
Marshall, J. & Speer, K. 2012 Closure of the meridional overturning circulation through southern ocean upwelling. Nature Geol. 5, 171–180.Google Scholar
Miller, R. C.1968 A thermally convecting fluid heated nununiformly from below. PhD thesis, Mass. Inst. Technol., Cambridge.Google Scholar
Mullarney, J. C., Griffiths, R. W. & Hughes, G. O. 2004 Convection driven by differential heating at a horizontal boundary. J. Fluid Mech. 516, 181–209.CrossRefGoogle Scholar
Munk, W. H. & Wunsch, C. 1998 Abyssal recipes. ii: energetics of tidal and wind mixing. Deep-Sea Res. 45, 1977–2010.Google Scholar
Park, Y. G. & Whitehead, J. A. 1999 Rotating convection driven by differential bottom heating. J. Phys. Oceanogr. 29, 1208–1220.2.0.CO;2>CrossRefGoogle Scholar
Pedlosky, J. 1969 The linear theory of hte circulation of a stratified ocean. J. Fluid Mech. 25, 185–205.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics. Springer.CrossRefGoogle Scholar
Pedlosky, J., Whitehead, J. A. & Veitch, G. 1997 Thermally driven motions in a rotating stratified fluid: theory and experiment. J. Fluid Mech. 339, 391–411.Google Scholar
Pickart, R. S. 1992 Water mass components of the north atlantic deep western boundary current. Deep-Sea Res. 39, 1553–1572.Google Scholar
Rossby, T. 1965 On thermal convection driven by non-uniform heating from below: an experimental study. Deep-Sea Res. 12, 9–16.Google Scholar
Rossby, T. 1998 Numerical experiments with a fluid heated non-uniformly from below. Tellus 50A, 242–257.Google Scholar
Sandström, J. W. 1908 Dynamishce versuche mit merrwasser. Annu. Hydrogr. Marit. Meteorol. 36, 6–23.Google Scholar
Sandström, J. W. 1916 Meteorologische studien im schwedischen hochgebirge. Göteb. Kungl. Vetensk. Vitterh. Handl. 18, 1–48.Google Scholar
Sheard, G. J., Hussam, W. K. & Tsai, T. 2016 Linear stability and energetics of rotating radial horizontal convection. J. Fluid Mech. 795, 1–35.Google Scholar
Speer, K. & Whitehead, J. A. 1998 A gyre in a non-uniformly heated rotating fluid. Deep-Sea Res. 35, 1069–1077.Google Scholar
Stern, M. E. 1975 Ocean Circulation Physics. Academic.Google Scholar
Stewart, K. D.2012 The effect of sills and mixing on the meridional overturning circulation. PhD thesis, Australian National University.Google Scholar
Stommel, H. 1958 The abyssal circulation. Deep-Sea Res. 5, 80–82.Google Scholar
Stommel, H. & Arons, A. B. 1960a On the abyssal circulation of the world ocean. i: stationary planetary flow patterns on a sphere. Deep-Sea Res. 6, 140–154.Google Scholar
Stommel, H. & Arons, A. B. 1960b On the abyssal circulation of the world ocean. ii. an idealized model of the circulation pattern and amplitude in oceanic basins. Deep-Sea Res. 6, 217–233.Google Scholar
Stommel, H., Arons, A. B. & Faller, A. J. 1958 Some examples of stationary planetary flow patterns in bounded basins. Tellus 10, 179–187.Google Scholar
Sverdrup, H. U. 1947 Wind-driven currents in a barolinic ocean: with application to the equatorial currents of the eastern pacific. Proc. Natl Acad. Sci. USA 33, 318–326.Google Scholar
Tailleux, R. & Rouleau, L. 2010 The effect of mechanical stirring on horizontal convection. Tellus 62A, 138–153.Google Scholar
Talley, L. D., Pickard, G. L., Emergy, W. J. & Swift, J. H. 2011 Descriptive Physical Oceanography (6th Edn): An Introduction. Academic.Google Scholar
Thorpe, S. A. 2005 The Turbulent Ocean. Cambridge University Press.Google Scholar
Tsai, T., Hussam, W. K., Fouras, A. & Sheard, G. J. 2016 The origin of instability in enclosed horizontally driven convection. Intl J. Heat Mass Transfer 94, 509–515.CrossRefGoogle Scholar
Vonder Haar, T. H. & Oort, A. H. 1973 New estimate of annual poleward energy transport by northern hemisphere oceans. J. Phys. Oceanogr. 3, 169–172.Google Scholar
Wang, G., Xie, S.-P., Q, T. & Huang, R. X. 2011 Deep south china sea circulation. Geophys. Res. Lett. 38.CrossRefGoogle Scholar
Wang, W. & Huang, R. X. 2005 An experimental study on thermal circulation driven by horizontal differential heating. J. Fluid Mech. 540, 49–73.Google Scholar
Whitehead, J. A. & Pedlosky, J. 2000 Circulation and boundary layers in differentially heated rotating stratified fluid. Dyn. Atmos. Oceans 31, 1–21.Google Scholar
Whitehead, J. A. & Wang, W. 2008 A laboratory model of vertical ocean circulation driven by mixing. J. Phys. Oceanogr. 38, 1091–1106.Google Scholar
Winters, K. B. & Barkan, R. 2013 Available potential energy density for Boussinesq fluid flow. J. Fluid Mech. 714, 476–488.Google Scholar
Wunsch, C. 2005 The total meridional heat flux and its oceanic and atmospheric partition. J. Clim. 18, 4374–4380.CrossRefGoogle Scholar