Gyres are prominent surface structures in the global ocean circulation that often interact with the sea floor in a complex manner. Diagnostic methods, such as the depth-integrated vorticity budget, are needed to assess exactly how such model circulations interact with the bathymetry. Terms in the vorticity budget can be integrated over the area enclosed by streamlines to identify forces that spin gyres up and down. In this article we diagnose the depth-integrated vorticity budgets of both idealized gyres and the Weddell Gyre in a realistic global model. It is shown that spurious forces play a significant role in the dynamics of all gyres presented and that they are a direct consequence of the Arakawa C-grid discretization and the z-coordinate representation of the sea floor. The spurious forces include a numerical beta effect and interactions with the sea floor which originate from the discrete Coriolis force when calculated with the following schemes: the energy conserving scheme (ENE); the enstrophy conserving scheme (ENS); and the energy and enstrophy conserving scheme (EEN). Previous studies have shown that bottom pressure torques provide the main interaction between the depth-integrated flow and the sea floor. Bottom pressure torques are significant, but spurious interactions with bottom topography are similar in size. Possible methods for reducing the identified spurious topographic forces are discussed. Spurious topographic forces can be alleviated by using either a B-grid in the horizontal plane or a terrain-following vertical coordinate.

The annual mean net surface heat fluxes (NSHFs) from the ocean to the atmosphere play an important role in driving both atmospheric circulations and oceanic meridional overturning circulations. Those generated by historical forcing simulations using the UK HadGEM3-GC3.1 coupled climate model are shown to be relatively independent of resolution, for model horizontal grid spacings between 1 and 1/12 degree, and to agree well with those based on the DEEPC analyses for the period 2000-2009. Interpretations of the geographical patterns of the NSHFs are suggested that are based on relatively simple dynamical ideas. As a step toward investigation of their validity, we examine the contributions to the rate of change of the active tracers (potential temperature, salinity and potential density) from the main terms in their prognostic equations as a function of the active tracer and latitude. We find that the main contributions from vertical mixing occur in “near surface” layers and that, except at high latitudes, the time-mean advection of potential temperature and density is well anti-correlated with the sum of the surface fluxes and vertical diffusion. By contrast, the tracer budget for the salinity has at least four terms of comparable magnitude. The heat input by latitude bands is shown to be dominated by the NSHFs, the time-mean advection, and the equatorial Pacific. Expressions for global integrals of the salt and heat content tendencies due to advection as a function of salinity and potential temperature respectively are derived and shown to make contributions that should not be neglected.

A recognized deficiency of ocean models with a constant-depth vertical coordinate is for truncation errors in the advection scheme to result in spurious numerical mixing of tracers, which can be substantial larger than that prescribed by the model’s mixing scheme. The z~ vertical coordinate allows vertical levels to displace in a lagrangian fashion on time scales shorter than a few days, but reverts to fixed levels on longer timescales, and is intended to reduce numerical mixing from transient vertical motions such as internal waves and tides. An assessment of z~ in a ¼° global implementation of the NEMO model is presented. It is shown that, in the presence of near-inertial gravity waves in the North Atlantic, z~ significantly reduces eulerian vertical velocities with respect to those in a control simulation with the default z* vertical coordinate; that the vertical coordinate approaches an isopycnal, or adiabatic, surface on short timescales; and that both tendences are enhanced when the z~ timescale parameters are lengthened with respect to the default settings. Evaluation of an effective diapycnal diffusivity, based on density transformation rates, shows that numerical mixing is consistently reduced as the z~ timescales are lengthened. The realism of the model simulation with different timescale parameters is assessed in the global domain, and it is shown that drifts in temperature and salinity, and the spindown in z*of the Antarctic Circumpolar Current, are reduced with z~, without incurring significant penalties in other metrics such as the strength of the overturning circulation or sea ice cover.