Closing the energy cycle in an ocean model

• The energy cycle of an ocean model is closed.
• The energetics of resolved and unresolved variables is outlined.
• Energy transfers due to the equation of state are clarified.
• Idealised and realistic global model configurations are presented.

An effort is discussed to construct a realistic ocean model in Boussinesq approximation which features a closed energy cycle up to numerical precision errors. In such a model, the energy related to the mean variables interacts with all parameterised forms of energy without any spurious energy sources or sinks. First, the concept of the energetics of the model in terms of resolved and unresolved energy variables is outlined using potential and dynamical enthalpy instead of internal and potential energy and without use of the concept of available potential energy. The role of energy transfer terms due to the non-linear, compressible equation of state is clarified. Second, a discretisation of the primitive equations is described in which energy transfers of viscous dissipation and mixing parameterisations are exactly calculated. Third, the model performance is documented using idealised and realistic global model configurations.