A simple and self-consistent geostrophic-force-balance model of the thermohaline circulation with boundary mixing
A simple model of the thermohaline circulation (THC) is formulated, with the objective to represent explicitly the geostrophic force balance of the basinwide THC. The model comprises advective-diffusive density balances in two meridional-vertical planes located at the eastern and the western walls of a hemispheric sector basin. Boundary mixing constrains vertical motion to lateral boundary layers along these walls. Interior, along-boundary, and zonally integrated meridional flows are in thermal-wind balance. Rossby waves and the absence of interior mixing render isopycnals zonally flat except near the western boundary, constraining meridional flow to the western boundary layer. The model is forced by a prescribed meridional surface density profile. This two-plane model reproduces both steady-state density and steady-state THC structures of a primitive-equation model. The solution shows narrow deep sinking at the eastern high latitudes, distributed upwelling at both boundaries, and a western boundary current with poleward surface and equatorward deep flow. The overturning strength has a 2/3-power-law dependence on vertical diffusivity and a 1/3-power-law dependence on the imposed meridional surface density difference. Convective mixing plays an essential role in the two-plane model, ensuring that deep sinking is located at high latitudes. This role of convective mixing is consistent with that in three-dimensional models and marks a sharp contrast with previous two-dimensional models. Overall, the two-plane model reproduces crucial features of the THC as simulated in simple-geometry three-dimensional models. At the same time, the model self-consistently makes quantitative a conceptual picture of the three-dimensional THC that hitherto has been expressed either purely qualitatively or not self-consistently.
Additional Information© Author(s) 2012. This work is distributed under the Creative Commons Attribution 3.0 License. Published by Copernicus Publications on behalf of the European Geosciences Union. Received: 05 Aug 2011 – Discussion started: 24 Aug 2011. Revised: 07 Jan 2012 – Accepted: 11 Jan 2012 – Published: 27 Jan 2012. We thank Carsten Eden, Dallas Murphy, and the participants of the workshop "Advanced Scientific Writing" for comments on earlier versions of the manuscript. We also thank David Marshall for his thorough review. J. C. was supported through a scholarship by the Studienstiftung des Deutschen Volkes (German National Academic Foundation). The service charges for this open access publication have been covered by the Max Planck Society. Edited by: A. Schiller
Published - os-8-49-2012.pdf