Abstract
The authors consider a mathematical model for the coupled atmosphere-ocean system, namely, the coupled quasigeostrophic-flow-energy-balance model. This model consists of the large-scale quasigeostrophic oceanic flow model and the transport equation for oceanic temperature, coupled with an atmospheric energy-balance model. After reformulating this coupled model as a random dynamical system (cocycle property), it is shown that the coupled quasigeostrophic-energy balance fluid system has a random attractor, and under further conditions on the physical data and the covariance of the noise, the system is ergodic, namely, for any observable of the coupled atmosphere-ocean flows, its time average approximates the statistical ensemble average, as long as the time interval is sufficiently long.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 6, pp. 67–84, 2006.
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Du, A., Duan, J., Gao, H. et al. Ergodic dynamics of the coupled quasigeostrophic-flow-energy-balance system. J Math Sci 151, 2677–2688 (2008). https://doi.org/10.1007/s10948-008-0165-y
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DOI: https://doi.org/10.1007/s10948-008-0165-y