Long Waves and Cyclone Waves

TLDR

Disturbances in atmospheric systems can be decomposed into components, some of which grow exponentially over time. The analysis shows that atmospheric disturbances possess a dominant exponentially growing component that ultimately dictates the size, structure, and growth rate of cyclonic and long waves, highlighting inherent limits to weather forecasting.

Abstract

By obtaining complete solutions, satisfying all the relevant simultaneous differential equations and boundary conditions, representing small disturbances of simple states of steady baroclinic large-scale atmospheric motion it is shown that these simple states of motion are almost invariably unstable. An arbitrary disturbance (corresponding to some inhomogeneity of an actual system) may be regarded as analysed into ≥components≤ of a certain simple type, some of which grow exponentially with time. In all the cases examined there exists one particular component which grows faster than any other. It is shown how, by a process analogous to ≥natural selection≤, this component becomes dominant in that almost any disturbance tends eventually to a definite size, structure and growth-rate (and to a characteristic life-history after the disturbance has ceased to be ≥small≤), which depends only on the broad characteristics of the initial (unperturbed) system. The characteristic disturbances (forms of breakdown) of certain types of initial system (approximating to those observed in practice) are identified as the ideal forms of the observed cyclonc waves and long waves of middle and high latitudes. The implications regarding the ultimate limitations of weather forecasting are discussed.