论文标题
确定性和随机Euler-Boussinesq对流
Deterministic and Stochastic Euler-Boussinesq Convection
论文作者
论文摘要
流体对流中不同运动尺度之间相互作用的随机参数通常用于估计预测不确定性，这可能是由于模型分辨率不足或观察结果而引起的，尤其是在处理大气和海洋动力学方面，粘性和扩散的消散效应可忽略不计。本文为经典的Euler-Boussinesq（EBC）方程提供了三种不同类型的随机参数的家族，用于在垂直平面下重力下流动的浮力不可压缩的流体。这三个随机模型的灵感来自于早期对随机波动对运输的影响的启发，例如，参见Kraichnan [1968，1994]和Doering等。 [1994]。它们是从汉密尔顿原理的变体中得出的，当时引入了Stratonovich噪声时的确定性情况。这三个模型具有其相应的哈密顿结构的不同变体。一种变体（盐）引入随机运输。另一个变体（sflt）引入了随机\ emph {迫切}，而不是随机\ emph {transper}。第三种变体（La Salt）以麦基恩（McKean）的概率意义[1966]引入其随机运输中的非局部性。
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].
