Project on the Generalized Stability of Chemical Dynamics

The goal of the project on the GST of chemical systems is to understand the sensitivity of both the equilibrium and the time dependent states produced by interaction among advection, diffusion and chemical reactions. The chemical reaction/advection/diffusion system is non-normal but in contrast to fluid dynamical systems where the appropriate norm is quadratic; the appropriate measure of chemical abundance is the L1 or counting norm as is used in economics.

Farrell, B. F., & Ioannou, P. J. (2000). Perturbation Dynamics in Atmospheric Chemistry. Journal of Geophysical Research , Vol. 105 (No. D7), 9303-9320 . Journal of Geophysical Research.Abstract

Current understanding of how chemical sources and sinks in the atmosphere interact with the physical processes of advection and diffusion to produce local and global distributions of constituents is based primarily on analysis of chemical models. One example of an application of chemical models which has important implications for global changes in natural and anthropogenic sources. This sensitivity to perturbation is often summarized by quantities such as a mean lifetime of a chemical species estimated from reservoir turnover time or the decay rate of the least damped normal mode of the species estimated from reservoir turnover time or the decay rate of the least damped normal mode of the species obtained from cigenanalysis of the linear perturbation equations. However, the decay rate of the least damped normal mode or a mean lifetime does not comprehensively reveal the response of a system to perturbation. In this work, sensitivity to  perturbations of chemical equilibria is assessed in a comprehensive manner through analysis of the system propagator. When chemical perturbations are measured using the proper linear norms, it is found that the greatest disturbance to chemical equilibrium is achieved by introducing a single chemical species at a single location, and that this optimal perturbation can be easily found by a single integration of the transpose of the perturbation can be easily found by a single location, and that this optimal perturbation can be easily found by a single integration of the transpose of the dynamical system. Among other results are determination of species distributions produced by impulsive, constant, and stochastic forcing; release sites producing the greatest and least perturbation in a chosen constituent at another chosen site; and a critical assessment of chemical lifetime measures. These results are general and apply to any perturbations are sufficiently small that the perturbation dynamics are linear.