Turbulence: Inertial-Range Bounds and PDFs

9316798 Kraichnan根据本奖项，首席研究员将从事三个相关主题，以基本了解湍流叶栅过程：(1)寻找三维不可压缩N-S湍流惯性范围的标度指数的界限；(2)发展分析方法，预测在惯性范围内的跨距离速度差的统计数据；(3)速度、涡量和其他湍流量极值概率的理论和数值研究。第一个项目将系统地使用精确的多时间动态约束和统计上的多时间可实现不等式。第二个项目将利用非线性映射技术来近似概率分布函数和惯性距离上速度差的其他高阶统计量。第三个项目将使用非线性映射技术来估计湍流和其他非线性过程的概率分布函数的极值尾部的大小和灵敏度。这项研究将为大气科学中的各种问题提供重要的见解，包括改进次网格尺度过程的建模。***

9316798 Kraichnan Under this award, the principal investigator will pursue three related topics directed at fundamental understanding of turbulent cascade processes: (1) a search for bounds on scaling exponents of the inertial range of three-dimensional incompressible Navier- Stokes turbulence; (2) development of analytical methods for predicting statistics of velocity differences across distances that fall within the inertial range of scales; (3) theoretical and numerical study of the probability of extreme values of velocity, vorticity, and other quantities of turbulent flow. The first project will make systematic use of exact multi-time dynamical constraints and multi-time realizability inequalities on statistics. The second project will exploit nonlinear mapping techniques in order to approximate probability distribution functions and other high-order statistics of velocity differences across inertial-range distances. The third project will use nonlinear mapping techniques to estimate the magnitude and sensitivity of extreme-value tails of probability distribution functions for turbulence and other nonlinear processes. This research will provide important insights for a variety of problems in atmospheric sciences including improvement of the modeling of subgrid-scale processes. ***