zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stochastic dynamics of a coupled atmosphere-ocean model. (English) Zbl 1090.86003

Summary: 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.

86A10Meteorology and atmospheric physics
60H15Stochastic partial differential equations
76M35Stochastic analysis (fluid mechanics)
76U05Rotating fluids
86A05Hydrology, hydrography, oceanography