Prof. Peter Read

Abstract:

In this paper, we show that the behaviour of weakly nonlinear waves in a 2-layer model of baroclinic instability on an f-plane with varying viscosity is determined by a single, degenerate codimension three bifurcation. In the process, we show how previous studies, using the method of multiple scales to derive evolution equations for the slowly varying amplitude of the growing wave, arise as special limits of the general evolution description. A companion study will extend the results to a β-plane.

Abstract:

An analytical model, previously developed for investigating the propagation of equatorially-trapped waves on an equatorial beta-plane in a uniform zonal flow in the presence of Rayleigh friction and Newtonian cooling in the Earth's stratosphere, is applied to Jupiter's upper troposphere and lower stratosphere. By analogy with the Earth, a 'spectral window' is identified for each of the main classes of equatorial wave mode, suggesting a mode-selection criterion for the dominant modes observed in association with strong wave-zonal flow interactions in the stratosphere. The modes favoured by this approach are compared with recent observations of wave activity and the quasi-quadrennial oscillation (QQO) in Jupiter's tropical atmosphere. Two modes with zonal wavenumber k similar to 8-11 are identified which may correspond to: (i) an equatorial Rossby mode moving eastward at around 100 m s(-1): and (ii) a mixed Rossby-gravity mode which is similar to stationary in System III, apparently excited by a wave source moving with the zonal wind in the deep troposphere. A Kelvin mode is also predicted to be present, but observational evidence for this mode is lacking to date. A numerical model, capable of solving for wave structures and wave-zonal flow interactions in arbitrary zonal flows using a Hermite spectral method, is adapted to conditions in Jupiter's stratosphere. The latter numerical model is shown to successfully simulate a plausible QQO with a period around four Earth years, given a single pair of forced Kelvin and MRG modes with tropospheric amplitudes consistent with observations. This model demonstrates that the QQO may indeed result, at least in principle, from interactions of a small number of equatorially-trapped wave modes with the zonal flow in the stratosphere. The selection of wave modes taking part in this process is not unique, however, and the precise identification of the relevant modes from observations remains elusive. (C) 2000 Elsevier Science Ltd. All rights reserved.