Browsing by Author "Gao, Hongjun"

Now showing 1 - 8 of 8
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    Almost periodic passive tracer dispersion
    (1999-12) Gao, Hongjun; Duan, Jinqiao; Fu, Xinchu
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    Asymptotic dynamical difference between the nonlocal and local Swift-Hohenberg models
    (1998-08) Lin, Guoguang; Gao, Hongjun; Duan, Jinqiao; Ervin, Vincent J.
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    Dynamics of a coupled atmosphere-ocean model
    (2001-07) Gao, Hongjun; Duan, Jinqiao
    The coupled atmosphere-ocean system defines the environment we live. The research of this complex, nonlinear and multiscale system is not only scientifically challenging but also practically important. We consider a coupled atmosphere-ocean model, which involves hydrodynamics, thermodynamics and nonautonomous interaction at the air-sea interface. First, we show that the coupled atmosphere-ocean system is stable under the external fluctuation in the atmospheric energy balance relation. Then, we estimate the atmospheric temperature 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. Finally, we prove that the coupled atmosphere-ocean system has time-periodic, quasiperiodic and almost periodic motions, whenever the external fluctuation in the atmospheric energy balance relation is time-periodic, quasiperiodic and almost periodic, respectively. 25,1
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    Dynamics of quasi-geostrophic fluid motions with rapidly oscillating Coriolis force
    (2001-07) Gao, Hongjun; Duan, Jinqiao
    An averaging principle for quasi-geostrophic fluid motions with rapidly oscillating Coriolis force is proved. This result includes comparison estimate and convergence result between quasi-geostrophic fluid motions and its averaged fluid motions. This averaging principle provides an autonomous system as an approximation for the nonautonomous quasi-geostrophic flows with rapidly oscillating Coriolis force.
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    Dynamics of the thermohaline circulation under wind forcing
    (2001-07) Gao, Hongjun; Duan, Jinqiao
    The ocean thermohaline circulation, also called meridional overturning circulation, is caused by water density contrasts. This circulation has large capacity of carrying heat around the globe and it thus affects the energy budget and further affects the climate. We consider a thermohaline circulation model in the meridional plane under external wind forcing. We show that, when there is no wind forcing, the stream function and the density fluctuation (under appropriate metrics) tend to zero exponentially fast as time goes to infinity. With rapidly oscillating wind forcing, we obtain an averaging principle for the thermohaline circulation model. This averaging principle provides convergence results and comparison estimates between the original thermohaline circulation and the averaged thermohaline circulation, where the wind forcing is replaced by its time average. This establishes the validity for using the averaged thermohaline circulation model for numerical simulations at long time scales.
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    Nonlocal dynamics of passive tracer dispersion with random stopping
    (1999-02) Gao, Hongjun; Brannan, James R.; Duan, Jinqiao
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    Stochastic dynamics of a coupled atmosphere-ocean model
    (2002-02) Gao, Hongjun; Duan, Jinqiao; Schmalfuss, Bjorn
    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.