标题： 确定性和随机欧拉-布辛涅斯克对流 显示英文标题

标题： Deterministic and Stochastic Euler-Boussinesq Convection

摘要： 随机参数化流体对流中不同尺度运动之间的相互作用常用于估计预测不确定性，这种不确定性可能由于模型分辨率不足或观测不完整而产生，特别是在处理大气和海洋动力学时，粘性和扩散耗散效应可以忽略不计。 本文推导了一类三种不同类型的随机参数化方法，用于经典欧拉-伯努利（EBC）方程，该方程描述了在垂直平面中受重力作用的浮力不可压缩流体。 这三种随机模型受到早期关于随机波动对传输影响的研究启发，例如，Kraichnan [1968, 1994] 和 Doering 等人 [1994]。 它们在这里是从确定性情况下的哈密顿原理变体推导出来的，当引入Stratonovich噪声时。 这三个模型具有其相应哈密顿结构的不同变体。 一种变体（SALT）引入了随机输运。 另一种变体（SFLT）引入了随机\emph{强制}，而不是随机\emph{运输}。 第三种变体（LA SALT）在其随机输运中引入了非局部性，在McKean [1966] 的概率意义上。 显示英文摘要

摘要： Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to inadequate model resolution, or incomplete observations, especially in dealing with atmosphere and ocean dynamics, where viscous and diffusive dissipation effects are negligible. This paper derives a family of three different types of stochastic parameterisations for the classical Euler-Boussinesq (EBC) equations for a buoyant incompressible fluid flowing under gravity in a vertical plane. These three stochastic models are inspired by earlier work on the effects of stochastic fluctuations on transport, see, e.g., Kraichnan [1968, 1994] and Doering et al. [1994]. They are derived here from variants of Hamilton's principle for the deterministic case when Stratonovich noise is introduced. The three models possess different variants of their corresponding Hamiltonian structures. One variant (SALT) introduces stochastic transport. Another variant (SFLT) introduces stochastic \emph{forcing}, rather than stochastic \emph{transport}. The third variant (LA SALT) introduces nonlocality in its stochastic transport, in the probabilistic sense of McKean [1966].