In this paper, we investigate the averaging principle for a stochastic coupled fast-slow atmosphere-ocean model. Precisely, we will first prove regularity estimates and tightness of the slow variable. Then, we prove the ergodicity of the fast variable with the frozen slow variable. In the end, we prove that the slow variable converges weakly and strongly to the solution of the averaged equation, when the initial and boundary value conditions are weak or strong, respectively, as ε goes to zero.

中文翻译：

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随机耦合快慢大气-海洋模型的平均原理

在本文中，我们研究了随机耦合的快-慢大气-海洋模型的平均原理。准确地说，我们将首先证明慢变量的规律性估计和紧密性。然后，我们用冻结的慢变量证明快变量的遍历性。最后，我们证明了当初始条件和边界值条件分别为弱或强时，当ε趋于零时，慢变量弱收敛于平均方程的解和强收敛。