论文标题
随机热准整形模型的理论分析和数值近似
Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model
论文作者
论文摘要
本文研究了潜在的涡度动力学的平衡2D热准综合基（TQG）模型的随机版本的数学特性。这种随机TQG模型旨在作为在上海动力学计算模拟中未分辨自由度的动态创建的参数化的基础，当水平浮力梯度和测深量法会影响动力学时，尤其是在submessoscale（250m-------------------------------------------10km）。具体而言，我们选择了[1]中引入的盐（通过谎言传输的随机对流），并在[2,3]中应用于我们的建模方法。盐方法保留了开尔文循环定理和TQG的无数整体保护定律家族。盐算法的目的是量化观察到或合成数据的缩放过程中的不确定性，以便于在较高的尺度上用于计算模拟中。目前的工作提供了对液体转运（盐）的随机对流的热准真实性（TQG）方程的溶液特性的严格数学分析[4,5]。
This paper investigates the mathematical properties of a stochastic version of the balanced 2D thermal quasigeostrophic (TQG) model of potential vorticity dynamics. This stochastic TQG model is intended as a basis for parametrisation of the dynamical creation of unresolved degrees of freedom in computational simulations of upper ocean dynamics when horizontal buoyancy gradients and bathymetry affect the dynamics, particularly at the submesoscale (250m--10km). Specifically, we have chosen the SALT (Stochastic Advection by Lie Transport) algorithm introduced in [1] and applied in [2,3] as our modelling approach. The SALT approach preserves the Kelvin circulation theorem and an infinite family of integral conservation laws for TQG. The goal of the SALT algorithm is to quantify the uncertainty in the process of up-scaling, or coarse-graining of either observed or synthetic data at fine scales, for use in computational simulations at coarser scales. The present work provides a rigorous mathematical analysis of the solution properties of the thermal quasigeostrophic (TQG) equations with stochastic advection by Lie transport (SALT) [4,5].
