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地球物理流体流动中的波的非线性相互作用，即在大气和海洋中。波浪相互作用产生大尺度现象，如在热带平流层观测到的东风和西风之间的准两年一次的振荡，以及小尺度现象，如下坡风暴和山区湍流。准确地表示天气和气候模式中的波动效应是很重要的。我的研究目的是为我们提供对波浪影响的必要理解，以及它们的产生和传播机制。我目前感兴趣的课题之一是在气候模型中使用的参数化方案的发展，以表示由大气中部重力波产生的阻力。我目前在地球物理流体动力学领域的其他兴趣包括大气低层山波的演变，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，电离层是高层大气中离子和电子大量存在以影响波传播的区域。我的次要研究方向涉及求解偏微分方程的数值方法。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，我研究了应用于需要非均匀间距数值网格问题的高阶紧致有限差分方法，以及用于模拟包括流体对流和热扩散在内的物理过程的交替方向显式方法。我目前正在研究在流体模拟中使用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.