A multiscale modelling and simulation methodology for turbulent geophysical flows

我们在大气层的底部生活和呼吸，大气中既有气体，也有微小的尘埃和烟雾。我们的健康和环境受到极其动荡的大气的非常复杂的机制的影响。在阳光明媚的日子里，陆地变暖的速度比海洋快，海洋将冷空气从海洋上空拖到陆地上。通过这个过程，能量通过增强的湍流混合进行交换。飓风(和其他自然灾害)的湍动能对生命和环境造成破坏。要回答环境问题--例如飓风为什么会形成、全球气温为什么会升高、极地冰川融化的速度为什么会加快，或者海平面为什么会上升--在很大程度上取决于对大气中湍流混合和输送的全面了解。例如，为了预测二氧化碳(CO2)或其他污染物等重要成分的未来分布，人们需要知道它们的来源和汇，以及这些污染物在动荡的大气中是如何混合的。 然而，当大气模式(无论是大气污染模式还是天气预报模式)采用10-20公里分辨率的典型中尺度网格时，湍流混合机制受到严重影响。我们目前的建模和模拟技术不足以在这种截断的分辨率下表示湍流，并且还没有在大范围的尺度上实现截断物理的参数化的全面发展；注意，在增加能量的尺度和发生湍流混合的尺度之间存在大约1亿倍的系数。向前发展的一种方法是发展各种条件下大气边界层的湍流模式，并利用收集的关于湍流的详细知识来对中尺度气象模式的未分辨物理进行参数化。 我的研究计划包括基于小波的多尺度方法的基本发展及其在解释湍流和其他小尺度气象变率对预报中尺度现象的影响方面的应用。 因此，建议的研究旨在开发和开发一个健壮、可靠和计算高效的基于小波的新的动力核心，用于复杂地形上的非静力多尺度气象方法。与当前的大气模式相比，所提出的中尺度模拟方法将用多尺度小波基捕捉相当大比例的气流，并将剩余运动参数化。利用第二代小波变换，发展了一种用于中尺度模式内能量涡双向嵌套的多尺度参数化技术。这种新的小波方法将探索亚中尺度和亚大涡尺度现象，这是拟议发展的一个重要方面。 在大气模拟领域，在10-20公里分辨率的中尺度网格上忠实地对边界层涡或其他对流现象进行参数化是最具挑战性和要求最高的课题之一。同样，可以从卫星获得中尺度分辨率的气象数据；然而，将观测到的气象反馈纳入对亚中尺度(例如龙卷风)或微尺度(例如边界层涡)现象的预测是必要的，也是具有挑战性的。所提出的基于小波的多尺度方法在中尺度模式中动态嵌套湍流和其他小尺度气象变率的成功将推动当代大气模式的发展，从而为中尺度和微尺度天气现象的预报铺平一条新的途径。

We live and breathe at the bottom of an atmosphere that contains both gases and tiny particles of dust and smoke. Our health and environment are affected by the very complex mechanisms of the extremely turbulent atmosphere. On a sunny day, the land warms up faster than the ocean, which drags cool air from over the ocean to the land. Through this process, energy is exchanged via enhanced turbulent mixing. Turbulent kinetic energy of hurricanes (and other natural disasters) causes damage to lives and their environment. Answering environmental questions - such as why hurricanes develop, why global temperature increases, why the rate of melting polar ice has increased, or why sea level rises - leans heavily on the complete understanding of the turbulent mixing and transport in the atmosphere. For example, in order to project the future distribution of such vital ingredients as carbon-dioxide (CO2) or other pollutants, one needs to know their sources and sinks, and how these pollutants are mixed in the turbulent atmosphere. However, the turbulent mixing mechanism is brutally affected when atmospheric models (either air pollution or weather prediction) employ a typical mesoscale grid at 10-20 km resolution. Our current modelling and simulation techniques are inadequate for representing turbulence at this truncated resolution, and have yet to approach a comprehensive development for parameterizing the truncated physics across a wide range of scales; note, there is a factor of about 100 million between the scale at which energy is added and that at which turbulent mixing occurs. One way to move forward is through the development of turbulent models for the atmospheric boundary layer under various conditions, and to utilize the gathered detailed knowledge on turbulence to parameterize unresolved physics of mesoscale meteorological models. My research program encompasses fundamental developments on a wavelet based multiscale methodology and its application to explain the influence of turbulence and other small scale meteorological variability on forecasting meso-scale phenomena. The proposed research thus aims to develop and exploit a robust, reliable, and computationally efficient new wavelet based dynamical core for a non-hydrostatic multiscale meteorological methodology over complex terrains. In contrast to contemporary atmospheric models, the proposed mesoscale modelling approach will capture the significant proportion of the flow with a multi-scale wavelet basis, and the residual motion will be parameterized. A multiscale parameterization technique will be developed for a two-way nesting of energetic eddies within a mesoscale model, employing the second generation wavelet transform. This new wavelet method will explore both the sub-mesoscale and sub-LES scale phenomena, which is an important aspect of the proposed development. In the field of atmospheric modelling, a faithful parameterization of boundary layer eddies or other convective phenomena on a mesoscale grid of 10-20 km resolution is one of the most challenging and demanding topics. Similarly, meteorological data may be available on the mesoscale resolution from a satellite; however, incorporating the observed meteorological feedback into the prediction of sub-mesoscale (e.g. a tornado) or micro-scale (e.g. boundary layer eddies) phenomena is necessary and also challenging. The success of the proposed wavelet based multiscale methodology for dynamically nesting turbulence and other small scale meteorological variability in a mesoscale model will advance state-of-the-art contemporary atmospheric models, thereby paving a new avenue toward the prediction of the mesoscale and the microscale weather phenomena.