INTRODUCTION

One of the major concerns of the meteorologist is the degree of predictability of atmospheric motions. The classic remarks made by Lorenz (1963), in the now-celebrated paper in which deterministic equations were first shown to exhibit aperiodic and consequently unpredictable behaviour, that it may be impossible to predict the weather accurately beyond a few days, only too truly reflect the current state of affairs. Although the availability of very fast computers and greater accuracy of initial data have brought about some improvement in weather forecasts, there is still a disappointing limit on the length of time for which a weather prediction can be considered to be accurate. Nevertheless certain features of atmospheric motion are observed to persist for considerable lengths of time, usually associated with what are known as blocking situations (Berggren et al 1949); a notable persistent factor in another planetary atmosphere is Jupiter's Red Spot. Among the models proposed for these phenomena are modons (Fleierl et al 1981) and solitons (Maxworthy and Redekopp, 1976).

We shall not be concerned in this article with direct modelling of atmospheric predictability; instead we shall concentrate on phenomena occurring in simple models exposing the essential physical behaviour, and demonstrate that under certain conditions, coherent persistent behaviour is possible.

Cyclones, anticyclones and their associated frontal systems are a prominent feature of the mid-latitude westerlies of the Earth's lower atmosphere. Their importance as weather-bearing systems and more generally their role in the general circulation of the atmosphere is wellknown if not yet well understood. Their occurrence and rapidly changing behaviour is strongly influenced by the existence of largerscale “longwaves” which are remarkable for their persistence and coherence over longer periods of time. Both phenomena owe their existence to the availability of potential energy associated with the baroclinicity of the fluid, i.e. the non-coincidence of surfaces of constant gravitational potential and constant density, which is a possible equilibrium in a rotating system. Such an equilibrium is unstable and wave-like perturbations can develop at the expense of the potential energy if the trajectories of fluid particles are contained within the geopotentials and isopynals.