Toward Energetically Consistent Ocean Models

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

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Lars Czeschel Institut für Meereskunde, Universität Hamburg, Hamburg, Germany

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Dirk Olbers Alfred-Wegener-Institut für Polar und Meeresforschung, Bremerhaven, Germany

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Abstract

Possibilities to construct a realistic quasi-global ocean model in Boussinesq approximation with a closed energy cycle are explored in this study. In such a model, the energy related to the mean variables would interact with all parameterized forms of energy without any spurious energy sources or sinks. This means that the energy available for interior mixing in the ocean would be only controlled by external energy input from the atmosphere and the tidal system and by internal exchanges. In the current implementation of such a consistent model, however, numerical biases and sources due to the nonlinear equation of state violate energy conservation, resulting in an overall residual up to several percent. In three (approximately) consistent model versions with different scenarios of mesoscale eddy dissipation, the parameterized internal wave field provides between 2 and 3 TW for interior mixing from the total external energy input of about 4 TW, such that a transfer between 0.3 and 0.4 TW into mean potential energy contributes to drive the large-scale circulation in the model. In contrast, the wind work on the mean circulation contributes by about 1.8 TW to the large-scale circulation in all model versions. It is shown that the consistent model versions are more energetic than standard and inconsistent model versions and in better agreement with hydrographic observations.

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

Abstract

Possibilities to construct a realistic quasi-global ocean model in Boussinesq approximation with a closed energy cycle are explored in this study. In such a model, the energy related to the mean variables would interact with all parameterized forms of energy without any spurious energy sources or sinks. This means that the energy available for interior mixing in the ocean would be only controlled by external energy input from the atmosphere and the tidal system and by internal exchanges. In the current implementation of such a consistent model, however, numerical biases and sources due to the nonlinear equation of state violate energy conservation, resulting in an overall residual up to several percent. In three (approximately) consistent model versions with different scenarios of mesoscale eddy dissipation, the parameterized internal wave field provides between 2 and 3 TW for interior mixing from the total external energy input of about 4 TW, such that a transfer between 0.3 and 0.4 TW into mean potential energy contributes to drive the large-scale circulation in the model. In contrast, the wind work on the mean circulation contributes by about 1.8 TW to the large-scale circulation in all model versions. It is shown that the consistent model versions are more energetic than standard and inconsistent model versions and in better agreement with hydrographic observations.

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