Department of Mathematics, Center for Atmosphere Ocean Science, Courant Institute, New York University, 251 Mercer Street, New York, NY 10012, USA.
Philos Trans A Math Phys Eng Sci. 2013 Jan 13;371(1982):20120184. doi: 10.1098/rsta.2012.0184.
This paper motivates, develops and reviews elementary models for turbulent tracers with a background mean gradient which, despite their simplicity, have complex statistical features mimicking crucial aspects of laboratory experiments and atmospheric observations. These statistical features include exact formulas for tracer eddy diffusivity which is non-local in space and time, exact formulas and simple numerics for the tracer variance spectrum in a statistical steady state, and the transition to intermittent scalar probability density functions with fat exponential tails as certain variances of the advecting mean velocity are increased while satisfying important physical constraints. The recent use of such simple models with complex statistics as unambiguous test models for central contemporary issues in both climate change science and the real-time filtering of turbulent tracers from sparse noisy observations is highlighted throughout the paper.
本文提出、发展并回顾了具有背景平均梯度的紊流传质示踪剂的基本模型，这些模型虽然简单，但具有复杂的统计特征，模拟了实验室实验和大气观测的关键方面。这些统计特征包括示踪剂涡动扩散率的精确公式，该公式在空间和时间上是非局部的，统计稳态中示踪剂方差谱的精确公式和简单数值，以及随着某些平均速度的方差增加而过渡到间歇标量概率密度函数，具有胖指数尾部，同时满足重要的物理约束。本文强调了最近使用这些具有复杂统计特征的简单模型作为气候变化科学和从稀疏噪声观测中实时过滤紊流传质示踪剂的当代核心问题的明确测试模型的应用。
