On fluctuating momentum exchange in idealised models of air sea interaction
Résumé
The dynamics of three local models, for momentum transfer at the air-sea interface, is compared. The models differ by whether or not the ocean velocity is included in the shear calculation applied to the ocean and the atmosphere. All three cases are employed in climate or ocean simulations. Analytic calculations for the models with deterministic and random forcing (white and coloured) are presented. The short term behaviour is similar in all models, which only small quantitative differences, while the long-term behaviour differs qualitatively between the models. The fluctuation-dissipation-relation, which 5 connects the fast atmospheric motion to the slow oceanic dynamics, is established for all models with random forcing. The fluctuation-dissipation-theorem, which compares the response to an external forcing to internal fluctuations is established for a white-noise forcing and a coloured forcing when the phase space is augmented by the forcing variable. Using results from numerical integrations of stochastic differential equations it is shown that the fluctuation-theorem, which compares the probability of positive to negative fluxes of the same magnitude, averaged over time-intervals of varying length, holds for the 10 energy gained by the ocean from the atmosphere.
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