Lattice models of advection-diffusion.
Lattice models of advection-diffusion.
复制标题
平流扩散的格子模型。
作者：
R. Pierrehumbert
我们提出了一个合成的理论结果，关于被动示踪剂的浓度的概率分布的扩散和平流的空间平滑的随时间变化的流。自由衰减的情况下，与平衡的情况下。介绍了一个计算效率高的对流扩散模型，并用于测试和探索理论思想的局限性。结果表明，自由衰减情况下的概率分布有厚尾，这比指数衰减慢。加性强迫的情况下，有一个高斯核心和指数的尾巴，完全符合先前的理论预期。的大小和影响的时间波动的条件扩散和耗散的分析，显示这些波动的重要性，在管理的形状的尾巴。文中还给出了关于耗散概率分布和浓度涨落空间标度性质的一些结果。虽然格子模型只适用于光滑流在本工作中，它是很容易适用于涉及粗糙流的问题，和化学反应示踪剂。(c)2000年美国物理学会。
We present a synthesis of theoretical results concerning the probability distribution of the concentration of a passive tracer subject to both diffusion and to advection by a spatially smooth time-dependent flow. The freely decaying case is contrasted with the equilibrium case. A computationally efficient model of advection-diffusion on a lattice is introduced, and used to test and probe the limits of the theoretical ideas. It is shown that the probability distribution for the freely decaying case has fat tails, which have slower than exponential decay. The additively forced case has a Gaussian core and exponential tails, in full conformance with prior theoretical expectations. An analysis of the magnitude and implications of temporal fluctuations of the conditional diffusion and dissipation is presented, showing the importance of these fluctuations in governing the shape of the tails. Some results concerning the probability distribution of dissipation, and concerning the spatial scaling properties of concentration fluctuation, are also presented. Though the lattice model is applied only to smooth flow in the present work, it is readily applicable to problems involving rough flow, and to chemically reacting tracers. (c) 2000 American Institute of Physics.