Mathematical Problems in Fluid Dynamics

NSF#DMS-9802611PI。P.Constantin摘要-我们建议扩展关于边界驱动的Navier-Stokes湍流中体积耗散变分界的工作，特别关注Rayleigh-Benard对流。我们打算研究旋转和普朗特数变化对高瑞利数湍流的影响。我们建议用解析和数值方法研究Navier-Stokes湍流中广义结构函数的标度，并将结果与简单随机模型的结果进行比较。我们建议用解析和数值方法研究可压缩耗散活动标量和准地转不可压缩活动标量的奇异性和动力学的形成。我们还建议研究颗粒动力学模型及其与实验数据的关系。本建议旨在了解流体中的非线性现象。了解这些现象对于从天气预报、气候和环境研究、湍流燃烧(例如发动机)到宇宙中质量分布的宇宙学问题等领域都是至关重要的。本提案的研究对象代表了挑战或超越当今最强大的计算系统能力的领域；提案的目的是发展物理数学、理论和数值模型，从而在我们进行计算机模拟的能力方面取得进展。NSF#DMS-9802611PI。P.Constantin摘要-我们建议扩展关于边界驱动的Navier-Stokes湍流中体积耗散变分界的工作，特别关注Rayleigh-Benard对流。我们打算研究旋转和普朗特数变化对高瑞利数湍流的影响。我们建议用解析和数值方法研究Navier-Stokes湍流中广义结构函数的标度，并将结果与简单随机模型的结果进行比较。我们建议用解析和数值方法研究可压缩耗散活动标量和准地转不可压缩活动标量的奇异性和动力学的形成。我们还建议研究颗粒动力学模型及其与实验数据的关系。本建议旨在了解流体中的非线性现象。了解这些现象对于从天气预报、气候和环境研究、湍流燃烧(例如发动机)到宇宙中质量分布的宇宙学问题等领域都是至关重要的。本提案的研究对象代表了挑战或超越当今最强大的计算系统能力的领域；提案的目的是发展物理数学、理论和数值模型，从而在我们进行计算机模拟的能力方面取得进展。

NSF #DMS-9802611PI. P. ConstantinAbstract-------- We propose to extend work on variational bounds for bulkdissipation in boundary driven Navier-Stokes turbulence, with particularattention to Rayleigh-Benard convection. We intend to investigate the effect of rotation and of change in Prandtl number on high Rayleighnumber turbulence. We propose to investigate analytically and numericallythe scaling of generalized structure functions in Navier-Stokes turbulence and compare the results with those of simple stochastic models. We propose to study analytically and numerically the formation of singularitiesand dynamics of compressible dissipative active scalars and of quasi-geostrophic incompressible active scalars. We also propose to investigate models of granular dynamics and their relation to experimental data. The present proposal is aimed at the understandingof nonlinear phenomena in fluids. Understanding these phenomena is essentialto areas that range from weather prediction, climate and environmental studies, turbulent combustion (as for instance in engines) to the cosmological question of mass distribution in the universe. The objects of study in this proposal represent areas that challenge or lie beyond the capabilities of the most powerful computing systems available today; the proposal aim is to develop physical mathematicstheory and numerical models that will yield progress in our ability to perform computer simulations. NSF #DMS-9802611PI. P. ConstantinAbstract-------- We propose to extend work on variational bounds for bulkdissipation in boundary driven Navier-Stokes turbulence, with particularattention to Rayleigh-Benard convection. We intend to investigate the effect of rotation and of change in Prandtl number on high Rayleighnumber turbulence. We propose to investigate analytically and numericallythe scaling of generalized structure functions in Navier-Stokes turbulence and compare the results with those of simple stochastic models. We propose to study analytically and numerically the formation of singularitiesand dynamics of compressible dissipative active scalars and of quasi-geostrophic incompressible active scalars. We also propose to investigate models of granular dynamics and their relation to experimental data. The present proposal is aimed at the understandingof nonlinear phenomena in fluids. Understanding these phenomena is essentialto areas that range from weather prediction, climate and environmental studies, turbulent combustion (as for instance in engines) to the cosmological question of mass distribution in the universe. The objects of study in this proposal represent areas that challenge or lie beyond the capabilities of the most powerful computing systems available today; the proposal aim is to develop physical mathematicstheory and numerical models that will yield progress in our ability to perform computer simulations.