Quantifying long time statistical properties of a few fluid models

量化一些流体模型的长期统计特性

• 批准号: 1008852
• 负责人: Xiaoming Wang
• 金额: $ 27.15万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1008852&HistoricalAwards=false
• 关键词: Quantifying; long; time; statistical; properties

WangDMS-1008852 The principal investigator and colleagues study the issue ofquantifying the long-time statistical properties of a fewprototype fluid systems via long-time statistical properties ofsuitable discrete dynamical systems related to temporal and/orspatial approximations. The physical problems considered are theRayleigh-Benard convection at large Prandtl number and/or smallEkman number regime, and a few related simplified models. Inparticular, the methodology developed is applied to numericallyquantify an important physical long-time statistical quantity,the averaged heat transport, in a few convection models. The keyissue here is the design, analysis and implementation of schemesthat are efficient and convergent (in the sense that thestationary statistical properties of the discrete system convergeto those of the underlying system). Approximating long-timebehavior of large complex systems is a well-known challengebecause small errors could accumulate and amplify. Additionaldifficulties related to multiple scales (induced by large Prandtlnumber, small Ekman number, large Rayleigh number), andgeneralised dynamical system (such as the 3D Boussinesq system)are also addressed. Suitable random perturbations of the fluidsystems are considered in order to ensure convergence to thephysically relevant long-time behaviour. Quantifying long-time statistical properties is of greatimportance in applications. Besides well-known applications inclassical turbulence theory, it is also extremely important inclimate studies because the predicted climate is the long-timestatistical behaviour of the underlying climate model. Themodels to be investigated, although far from practical climatemodels, share several important mechanisms that are crucial torealistic climate models, such as energy-preserving nonlinearadvection, rotation, convection, dissipation/damping and forcing. A clearer understanding of long-time statistical behavior in thissetting helps us better understand many geophysical fluidphenomena, and provides guidelines for accurate numerical studyof climate changes. The project also provides abundantopportunities for graduate students, including student fromunderrepresented group, to participate in the modeling, analysis,and computation of many physically motivated problems.

WangDMS-1008852 主要研究者及其同事研究了通过与时间和/或空间近似相关的合适离散动力系统的长时间统计特性来量化几个原型流体系统的长时间统计特性的问题。 所考虑的物理问题是在大普朗特数和/或小埃克曼数区域的Rayleigh-Benard对流，以及一些相关的简化模型。 特别是，所开发的方法被施加到numericalquantifying一个重要的物理长期统计量，平均热传输，在几个对流模式。 这里的关键问题是设计、分析和实现高效和收敛的方案（在这个意义上，离散系统的平稳统计特性收敛于底层系统的平稳统计特性）。 近似大型复杂系统的长期行为是一个众所周知的挑战，因为小的错误可能会积累和放大。 此外，还讨论了与多尺度（由大Prandtl数、小Ekman数、大Rayleigh数引起）和广义动力系统（如三维Boussinesq系统）有关的困难。 适当的随机扰动的流体系统被认为是为了确保收敛到thephysically相关的长期行为。 量化长时间统计特性在实际应用中具有重要意义。 除了经典湍流理论的著名应用外，它在气候研究中也是极其重要的，因为预测的气候是基础气候模式的长期统计行为。 这些模式虽然与实际气候模式相差甚远，但它们都具有一些对实际气候模式至关重要的机制，如能量守恒的非线性平流、旋转、对流、耗散/阻尼和强迫。更清楚地了解这种情况下的长期统计行为有助于我们更好地理解许多地球物理流体现象，并为气候变化的精确数值研究提供指导。 该项目还为研究生，包括来自代表性不足群体的学生提供了丰富的机会，参与许多物理动机问题的建模，分析和计算。