We are grateful to Chris Hughes for pointing out an inconsistency in section 6 and to David Munday and Laure Zanna for help with setting up the MITgcm calculations. The comments of two anonymous reviewers led to an improved and more focused manuscript. Financial supported was provided by the U.K. Natural Environment Research Council. The computations described in section 7 were performed at the Oxford Supercomputing Centre, University of Oxford.
Adcroft, A. J., C. N. Hill, and J. C. Marshall, 1999: A new treatment of the Coriolis terms in C-grid models at both high and low resolutions. Mon. Wea. Rev., 127, 1928–1936.
Arakawa, A., 1966: Computational design for long-term numerical integration of the equations of fluid motion: Two-dimensional incompressible flow. Part 1. J. Comput. Phys., 1, 119–143.
Cessi, P., G. Ierley, and W. Young, 1987: A model of the inertial recirculation driven by potential vorticity anomalies. J. Phys. Oceanogr., 17, 1640–1652.
Hughes, G. O., A. M. C. Hogg, and R. W. Griffiths, 2009: Available potential energy and irreversible mixing in the meridional overturning circulation. J. Phys. Oceanogr., 39, 3130–3146.
Marshall, J. C., C. Hill, L. Perelman, and A. Adcroft, 1997: Hydrostatic, quasihydrostatic, and nonhydrostatic ocean modeling. J. Geophys. Res., 102, 5733–5752.
Mellor, G. L., T. Ezer, and L. Y. Oey, 1994: The pressure gradient conundrum of sigma coordinate ocean models. J. Atmos. Oceanic Technol., 11, 1126–1134.
Munday, D. R., and D. P. Marshall, 2005: On the separation of a barotropic western boundary current from a cape. J. Phys. Oceanogr., 35, 1726–1743.
Stommel, H., and A. B. Arons, 1960: 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, 140–154.
Sverdrup, H. U., 1947: Wind-driven currents in a baroclinic ocean; with application to the equatorial currents of the eastern pacific. Proc. Natl. Acad. Sci. USA, 22, 318–326.
Tailleux, R., 2009: On the energetics of stratified turbulent mixing, irreversible thermodynamics, Boussinesq models and the ocean heat energy controversy. J. Fluid Mech., 638, 339–382.
Veronis, G., 1966: Wind-driven ocean circulation. Part II: Numerical solutions of the non-linear problem. Deep-Sea Res., 13, 31–55.
Note that this argument is distinct from that presented by Pedlosky (1965) in which trapping of short Rossby waves generated at the western boundary by either friction or inertia is used to explain western intensification.
Note that the neglected term of O(D2/L2) need not be aligned with k × ∂Ah/∂z. Thus, the notation O(·) should be interpreted as allowing for arbitrary direction in the neglected terms.