2004/08/27 by Jinqiao Duan, J. Duan, Duan, J. +6 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #34D35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Primary 60H15 #Secondary 86A05 #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.AP #math.DS #msc:34D35 #msc:60H15 #msc:86A05
paper · pdf · doi:10.48550/arxiv.math/0408386
Submitted to Chorin II Proceedings
arxiv created 2004/08/27 · openalex publication_date 2004/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The investigation of the coupled atmosphere-ocean system is not only scientifically challenging but also practically important. We consider a coupled atmosphere-ocean model, which involves hydrodynamics, thermodynamics, and random atmospheric dynamics due to short time influences at the air-sea interface. We reformulate this model as a random dynamical system. First, we have shown that the asymptotic dynamics of the coupled atmosphere-ocean model is described by a random climatic attractor. Second, we have estimated the atmospheric temperature evolution under oceanic feedback, in terms of the freshwater flux, heat flux and the external fluctuation at the air-sea interface, as well as the earth's longwave radiation coefficient and the shortwave solar radiation profile. Third, we have demonstrated that this system has finite degree of freedom by presenting a finite set of determining functionals in probability. Finally, we have proved that the coupled atmosphere-ocean model is ergodic under suitable conditions for physical parameters and randomness, and thus 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.