Revisiting the Energetics of the Ocean in Boussinesq Approximation

Carsten Eden Institut für Meereskunde, Universität Hamburg, Hamburg, Germany

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Abstract

Following a suggestion by Tailleux, a consistent formulation of internal energy, the first law of thermodynamics, and the thermodynamic potentials for an ocean in Boussinesq approximation with a nonlinear equation of state is given. A modification of the pressure work in the first law is the only necessary modification from which all thermodynamic potentials and thermodynamic relations follow in a consistent way. This treatment of thermodynamics allows for a closed and explicit formulation of conservation equations for dynamic and potential reservoirs of both enthalpy and internal energy, which differentiate approximately reversible from irreversible effects on internal energy, and allows for a formulation of a closed energy cycle on which energetically consistent ocean models can be based on.

Corresponding author address: Carsten Eden, Institut für Meereskunde, Universität Hamburg, Bundesstraße 53, 20146 Hamburg, Germany. E-mail: carsten.eden@zmaw.de.

This article is included in the In Honor of Bach-Lien Hua: Ocean Scale Interactions special collection.

Abstract

Following a suggestion by Tailleux, a consistent formulation of internal energy, the first law of thermodynamics, and the thermodynamic potentials for an ocean in Boussinesq approximation with a nonlinear equation of state is given. A modification of the pressure work in the first law is the only necessary modification from which all thermodynamic potentials and thermodynamic relations follow in a consistent way. This treatment of thermodynamics allows for a closed and explicit formulation of conservation equations for dynamic and potential reservoirs of both enthalpy and internal energy, which differentiate approximately reversible from irreversible effects on internal energy, and allows for a formulation of a closed energy cycle on which energetically consistent ocean models can be based on.

Corresponding author address: Carsten Eden, Institut für Meereskunde, Universität Hamburg, Bundesstraße 53, 20146 Hamburg, Germany. E-mail: carsten.eden@zmaw.de.

This article is included in the In Honor of Bach-Lien Hua: Ocean Scale Interactions special collection.

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