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The Lorenz system was derived on the basis of a model of convectiveatmospheric motions and may serve as a paradigmatic model for considering acomplex climate system. In this study, we formulated the thermodynamicefficiency of convective atmospheric motions governed by the Lorenz system bytreating it as a non-equilibrium thermodynamic system. Based on the fluidconservation equations under the Oberbeck-Boussinesq approximation,the worknecessary to maintain atmospheric motion and heat fluxes at the boundaries werecalculated. Using these calculations, the thermodynamic efficiency wasformulated for stationary and chaotic dynamics. The numerical results showthat, for both stationary and chaotic dynamics, the efficiency tends toincrease as the atmospheric motion is driven out of thermodynamic equilibriumwhen the Rayleigh number increases. However, it is shown that the efficiency isupper bounded by the maximum efficiency, which is expressed in terms of theparameters characterizing the fluid and the convective system. The analysis ofthe entropy generation rate was also performed for elucidating the differencebetween the thermodynamic efficiency of conventional heat engines and thepresent atmospheric heat engine. It is also found that there exists an abruptdrop in efficiency at the critical Hopf bifurcation point, where the dynamicschange from stationary to chaotic. These properties are similar to those foundpreviously in Malkus-Lorenz waterwheel system.

Thermodynamic efficiency of atmospheric motion governed by Lorenz system