Modeling Mesoscale Convection by Coupled Nonlinear Systems

由于大气系统是非线性的，有时在性质上是混沌的，因此对大气系统基本方面的研究变得困难。因此，数值系统（被称为低阶模型；LOMs）在提供相对简单的数学解决方案的同时，仍然保持了大气流动的基本特征，这是理解潜在物理的有价值的研究工具。主要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呈现。提出了一种构建大气环流LOMs的方法，即使用简单易懂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质，并具有各种流体动力学解释，其中著名的洛伦兹模型就是其中之一。提出的研究将解决发展物理健全的大气环流低阶模式的问题，特别关注中尺度浅对流（MSC）的建模。骨髓间充质干细胞是由多种复杂的过程混合而成，这些过程在骨髓间充质干细胞进化中的作用尚不清楚。目标是最终从负责特定进程的陀螺仪或陀螺仪块组装一个MSC模型。

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.