Numerical and analytical studies of geophysical flows and nonlinear waves

我的研究范围很广，从理论流体动力学到数值分析。我的主要研究重点是在地球物理流体流动，即波的非线性相互作用，在大气层和海洋中。波的相互作用引起大规模的现象，如在热带平流层观察到的东风和西风之间的准两年一次的振荡，以及较小规模的现象，如下坡风暴和山区湍流。波浪效应在天气和气候模式中的精确表达是很重要的。我的研究旨在为我们提供所需的波的影响，以及它们的产生和传播的机制的理解。我正在进行的感兴趣的主题之一是参数化方案的发展，用于气候模式，以代表拖曳力，结果重力波在中层大气。我目前在地球物理流体动力学领域的其他兴趣包括大气层低层中山波的演变，大气和海洋中的行星波相互作用，以及电离层中的重力波传播，在高层大气中，离子和电子的数量足以影响波的传播。我的第二个研究方向是用数值方法求解部分波的传播。微分方程我感兴趣的方法适用于各种物理问题，包括但不限于地球物理流体动力学。最近，我研究了高阶紧致有限差分法应用于需要数值网格与非均匀间距的问题，和交替方向明确的方法模拟物理过程，包括流体对流和热扩散。我目前正在研究在流体模拟中使用的非反射边界条件的实现。

My research spans a wide range of subjects, from theoretical fluid dynamics to numerical analysis. My primary research focus is on nonlinear interactions of waves in geophysical fluid flows, i.e., in the atmosphere and oceans. Wave interactions give rise to large-scale phenomena, such as the quasi-biennial oscillation between easterly and westerly winds that is observed in the tropical stratosphere, and smaller-scale phenomena, such as downslope windstorms and turbulence over mountains. It is important that wave effects are represented accurately weather and climate models. My investigations aim to provide us with the needed understanding of  the effects of the waves, as well as the mechanisms for their generation and propagation.One of my ongoing topics of interest is the development of parameterization schemes that are used in climate models to represent the drag force that results from gravity waves in the middle atmosphere. My other current interests in the field of geophysical fluid dynamics include the evolution of mountain waves in the lower levels of the atmosphere, planetary wave interactions in the atmosphere and ocean, and gravity wave propagation in the ionosphere, the region in the upper atmosphere where ions and electrons are present in large enough quantities to affect wave propagation.My secondary line of research involves numerical methods for solving partial differential equations. The methods that interest me are applicable to a variety of physical problems including, but not limited to, geophysical fluid dynamics. Recently I have studied high-order compact finite difference methods applied to problems which require numerical grids with non-uniform spacing, and alternating-direction explicit methods for modelling physical processes that include both fluid convection and heat diffusion. I am currently investigating the implementation of non-reflecting boundary conditions for use in fluid simulations.