Abstract
A post bifurcation, finite-amplitude analysis of baroclinic instability is undertaken. The original motivation was to explore the possibility that baroclinic waves may be excited for a value of the wind shear below that predicted by linear theory. Accordingly, the post instability behavior of a linear combination of baroclinic waves, which are the natural eigenfunctions associated with the linear problem, is examined, particular attention being paid to those configurations of wavevectors which have strong quadratic nonlinear interactions. The resulting patterns are known as hexagons in the literature, a term we shall use but with the understanding that such a term is only descriptive of the solution pattern when the motions are stationary. It is proven that, while hexagons can dominate the flow pattern, they cannot sustain subcritical motions. The introduction of a small amount of viscosity proves to be singular not only in the specification of the neutral curve but also by ensuring that the growth rate of the baroclinic wave is independent of its direction. In cases where sidewall boundaries do not quantize the spectrum (in the north-south direction) of available solutions, we find that the resulting flow patterns are likely to be irregular and time-dependent, due to a sharing of the available energy between many modes. Spatial modulation of the baroclinic waves can also be important and lead in some cases to a breakdown of the wave. When these effects are included, a novel technique for deriving the amplitude equations is exhibited.
