Modeling Mesoscale Convection by Coupled Nonlinear Systems

大气系统本质上是非线性的，有时甚至是混沌的，这使得大气系统的基本方面的研究变得困难。因此，数值系统(称为低阶模型；LOM)可以得到相对简单的数学解，同时仍然保持大气流动的基本特征，是理解基本物理的宝贵研究工具。首席研究人员的初步研究表明，大气现象的低阶模型可以以经典力学中称为Volterra陀螺仪的数学系统的形式提出。提出了一种构建大气环流LOM的积木式方法，即使用简单且易于理解的组件来构建复杂现象的模型。这些方程具有流体动力学方程的基本守恒性，并有不同的流体动力学解释，著名的洛伦兹模型就是其中之一。拟议的研究将解决建立物理上合理的低阶大气环流模式的问题，并特别注意模拟中尺度浅对流(MSC)。MSC是各种过程的复杂组合的结果，其在MSC进化中的作用尚不清楚。我们的目标是最终用陀螺仪或陀螺仪块组装出一个MSC模型，负责特定的过程。

The study of fundamental aspects of atmospheric systems is made difficult by the fact that these systems are nonlinear and sometimes chaotic in nature. Accordingly, numerical systems (known as low order models; LOMs) that lend themselves to relatively simple mathematical solutions while still maintaining the fundamental characteristics of the atmospheric flows are valuable research tools for understanding the underlying physics. Preliminary studies by the Principal Investigators indicate that low order models of atmospheric phenomena may be presented in the form of mathematical systems known in classical mechanics as Volterra gyrostats. A building block approach for the construction of LOMs of atmospheric circulations is proposed, whereby simple well-understood components are used to construct models of complex phenomena. These possess fundamental conservation properties of fluid dynamic equations and have various fluid dynamic interpretations, the celebrated Lorenz model among them. The proposed research will address the problem of developing physically sound low-order models of atmospheric circulations with particular attention to modeling mesoscale shallow convection (MSC). MSC results from a complex mix of various processes whose roles in the evolution of MSC remain unclear. The goal is to eventually assemble a model of MSC from gyrostats, or blocks of gyrostats, responsible for particular processes.