Abstract. 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, with only small quantitative differences, while the long-term behaviour differs qualitatively between the models. The fluctuation–dissipation relation, which 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, we show that the fluctuation theorem, which compares the probability of positive to negative fluxes of the same magnitude, averaged over time intervals of varying lengths, holds for the energy gained by the ocean from the atmosphere.

中文翻译：

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海气相互作用理想模型中的波动动量交换

摘要。比较了三个局部模型的动力学，用于海气界面处的动量传递。这些模型的不同之处在于在应用于海洋和大气的剪切计算中是否包括海洋速度。所有三个案例都用于气候或海洋模拟。给出了具有确定性和随机强迫（白色和彩色）的模型的分析计算。所有模型的短期行为都相似，只有很小的数量差异，而模型之间的长期行为在质量上有所不同。对于所有具有随机强迫的模型，建立了将快速大气运动与缓慢海洋动力学联系起来的涨落-耗散关系。波动-耗散定理，将外部强迫的响应与内部波动进行比较，当相位空间通过强制变量增加时，为白噪声强制和有色强制建立。使用随机微分方程的数值积分结果，我们证明了波动定理，它比较了相同量级的正负通量的概率，在不同长度的时间间隔内进行平均，适用于海洋从大气中获得的能量.