Prediction of Probability Functions for Fluid Systems

这项建议的核心是开发和开发“映射闭合”，这是一种新的和强大的湍流流场特性统计模拟方法。闭合映射是基于将具有已知统计量的场连续扭曲为根据已知物理-动力学定律发展的流的近似值。与传统的分析方法相比，它有几个优点，特别是在预测这些场的统计性质方面，包括全概率分布函数(Pdf)。它可以对不太可能发生的事件给出有意义的估计，而且由于它可以跟踪物理空间中的结构，它可能会导致更真实的亚格子尺度表示。文中建议将该方法应用于二维湍流和准地转动力学控制的场的pdf。拟议的工作还包括调查所需计算的实用程序；出版一份面向教学的论文，使地球科学界更广泛地使用该方法的相关工具；以及评价其对次网格表示的适用性。尽管该方法的前两个应用与大规模气象学和海洋学特别相关，但Kraichnan在该方法上的工作一直受到其他学科的科学家的密切关注。他们已经认识到，它可以应用于宇宙中的大部分流体，这些流体在所有尺度的系统中处于湍流运动中。这包括那些正在经历非线性化学反应的人(如在燃烧模型中)，那些用于机械工程的人，以及那些在行星科学和天体物理学中被考虑的人。

This proposal is centered about development and exploitation of "mapping closure", a novel and powerful method for statistical modeling of the properties of turbulent flow fields. Mapping closure is based on the continuous distortion of fields with known statistics into approximations of flows developing according to known physical-dynamic laws. It has several advan- tages over traditional analytical approaches, particularly with regard to the prediction of the statistical properties of such fields, including entire probability distribution functions (pdf's). It can give meaningful estimates of improbable events, and since it can track structures in physical space it may lead to more realistic subgrid-scale representations. It is proposed that the method be applied to pdf's of 2-dimensional turbulence and of fields governed by quasi-geostrophic dynamics. The pro- posed work also encompasses the investigation of practical procedures for the calculations required; the publication of a pedagogically oriented paper to make the method's associated tools more widely available to the geosciences community; and the evaluation of its applicablity to subgrid representations. Although the first two applications of the method are of particular relevance to large-scale meteorology and oceanography, Kraichnan's work on the method has been closely followed by scientists in other disciplines. They have recognized that it can be applied to the large percentage of the fluid in the universe that is in turbulent motion in systems of all scales. These include those undergoing non-linear chemical reactions (as in combustion models), those used in mechanical engineering, and those considered in planetary science and in astrophysics.