The conversion of barotropic to baroclinic tidal energy in the global abyssal ocean is calculated using three different formulations. The calculations are done both “offline,” that is, using externally given tidal currents to estimate the energy conversion, and “online,” that is, by using the formulations to parameterize linear wave drag in a prognostic tidal model. All three schemes produce globally integrated offline dissipation rates beneath 500-m depth of ~0.6–0.8 TW for the M2 constituent, but the spatial structures vary significantly between the parameterizations. Detailed investigations of the energy transfer in local areas confirm the global results: there are large differences between the schemes, although the horizontally integrated conversion rates are similar. The online simulations are evaluated by comparing the sea surface elevation with data from the TOPEX/Poseidon database, and the error is then significantly lower when using the parameterization provided by Nycander than with the other two parameterizations examined.

There is a growing realization that the nonlinear nature of the equation of state has a deep impact on the global ocean circulation; however, the understanding of the global effects of these nonlinearities remains elusive. This is partly because of the complicated formulation of the seawater equation of state making it difficult to handle in theoretical studies. In this paper, a hierarchy of polynomial equations of state of increasing complexity, optimal in a least squares sense, is presented. These different simplified equations of state are then used to simulate the ocean circulation in a global 2°-resolution configuration. Comparisons between simulated ocean circulations confirm that nonlinear effects are of major importance, in particular influencing the circulation through determination of the static stability below the mixed layer, thus controlling rates of exchange between the atmosphere and the ocean interior. It is found that a simple polynomial equation of state, with a quadratic term in temperature (for cabbeling), a temperature–pressure product term (for thermobaricity), and a linear term in salinity, that is, only four tuning parameters, is enough to simulate a reasonably realistic global circulation. The best simulation is obtained when the simplified equation of state is forced to have an accurate thermal expansion coefficient near the freezing point, highlighting the importance of polar regions for the global stratification. It is argued that this simplified equation of state will be of great value for theoretical studies and pedagogical purposes.