Preprints
https://doi.org/10.5194/esd-2020-82
https://doi.org/10.5194/esd-2020-82

  15 Dec 2020

15 Dec 2020

Review status: a revised version of this preprint is currently under review for the journal ESD.

Jarzynski equality and Crooks relation for local models of air-sea interaction

Achim Wirth1 and Florian Lemarié2 Achim Wirth and Florian Lemarié
  • 1Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI, 38000 Grenoble, France
  • 2Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble,France

Abstract. We show using a hierarchy of local models of air-sea interaction that the most prominent of the work theorems, the Jarzynski equality and the Crooks relation can be applied to air-sea interaction. In the more idealized models, with and without a Coriolis force, the variability is provided from a Gaussian white-noise which modifies the shear between the atmosphere and the ocean. The dynamics is Gaussian and the Jarzynski equality and Crooks relation can be obtained analytically solving stochastic differential equations. The more involved model consists of interacting atmospheric and oceanic boundary-layers, where only the dependence on the vertical direction is resolved, the turbulence is modeled through standard turbulent models and the stochasticity comes from a randomized drag coefficient. It is integrated numerically and can give rise to a non-Gaussian dynamics. Also in this case the Jarzynski equality allows for calculating a dynamic-beta βD of the turbulent fluctuations (the equivalent of the thermodynamic-beta β = (kBT)−1 in thermal fluctuations). The Crooks relation gives the βD as a function of the magnitude of the work fluctuations. It is well defined (constant) in the Gaussian models and can show a slight variation in the more involved models. This demonstrates that recent concepts of stochastic thermodynamics used to study micro-systems subject to thermal fluctuations can further the understanding of geophysical fluid dynamics with turbulent fluctuations.

Achim Wirth and Florian Lemarié

 
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Achim Wirth and Florian Lemarié

Achim Wirth and Florian Lemarié

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Short summary
We show that the modern concepts of non-equilibrium statistical mechanics can be applied to large scale environmental fluid dynamics, where fluctuations are not thermal but come from the turbulence. The work theorems developed by Jarzynski and Crooks are applied to air-sea interaction. Rather than looking at average values of the thermodynamic variables they consider their probability density functions which allow to replace the inequalities of equilibrium statistical mechanics by equalities.
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