Mathematical Problems in Fluid Dynamics

NSF #DMS-9802611PI。P. Constantin摘要- 我们建议扩展边界驱动的Navier-Stokes湍流中体积耗散的变分边界的工作，特别注意Rayleigh-Benard对流。本文研究了旋转和普朗特数变化对高瑞利数湍流的影响。本文对Navier-Stokes湍流中广义结构函数的标度性进行了解析和数值研究，并与简单随机模型的结果进行了比较。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。我们还建议调查模型的颗粒动力学和实验数据的关系。 目前的建议是为了理解流体中的非线性现象。理解这些现象对于从天气预报、气候和环境研究、湍流燃烧（例如发动机中的湍流燃烧）到宇宙质量分布的宇宙学问题等领域至关重要。本提案中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;该提案的目的是开发物理数学理论和数值模型，以提高我们进行计算机模拟的能力。NSF #DMS-9802611PI。P. Constantin摘要- 我们建议扩展边界驱动的Navier-Stokes湍流中体积耗散的变分边界的工作，特别注意Rayleigh-Benard对流。本文研究了旋转和普朗特数变化对高瑞利数湍流的影响。本文对Navier-Stokes湍流中广义结构函数的标度性进行了解析和数值研究，并与简单随机模型的结果进行了比较。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。我们还建议调查模型的颗粒动力学和实验数据的关系。 目前的建议是为了理解流体中的非线性现象。理解这些现象对于从天气预报、气候和环境研究、湍流燃烧（例如发动机中的湍流燃烧）到宇宙质量分布的宇宙学问题等领域至关重要。本提案中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;该提案的目的是开发物理数学理论和数值模型，以提高我们进行计算机模拟的能力。

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.