Abstract
A simple model of the tropospheric circulation, based on a 10-level primitive equation model, is forced by linearly relaxing the potential temperature toward an idealized, zonally symmetric equilibrium field. The model equations are integrated in time until a statistically steady state is obtained. The local relationship between the state of the background flow, the direction of wave propagation, and subsequent wave breaking at the tropopause level is then investigated. Maps of potential vorticity (PV) on isentropic surfaces are analyzed and all four different types of wave breaking described recently by Peters and Waugh are shown to occur. It is found that cyclonic wave breaking events are usually initiated by poleward fluxes of wave activity, and anticyclonic events by equatorward fluxes. Composites are then used to show that equatorward fluxes are associated with a jet that is locally broad and weak, with relatively strong isentropic PV gradients to its equatorward flank. By contrast, poleward fluxes are associated with a narrow, strong jet, with very weak or even negative PV gradients on its equatorward side. It is argued that this result is consistent with nonlinear critical-layer theory, as under certain conditions an isolated region of homogenized potential vorticity must remain a perfect reflector of wave activity for all time.
The variability exhibited by the zonal flow field is then investigated using a cross-sectional EOF method. The first EOF is found to have similar structure in the latitude–height plane to the baroclinic waves themselves, and describes much of the variability associated with them. The second EOF has structure that corresponds to a sharp, narrow jet in its positive phase and a weak, broad jet in its negative phase. Its phase is shown to be well correlated with the wave activity flux index, with the maximum occurring at a space and time lag, with the phase of the EOF preceding the index. Most of the variability associated with this EOF occurs on the scale of zonal wavenumbers 2–4, suggesting that the direction of meridional propagation of the baroclinic waves is determined locally. Strikingly, the phase of the second EOF propagates in a wavelike manner, with wavenumber and period (≈11–14 days) quite distinct from those of the baroclinic waves. Individual phase maxima of these long waves can persist for up to ≈20–25 days, as they do not decay rapidly due to downstream radiation.
Corresponding author address: Dr. J. G. Esler, Centre for Atmospheric Science, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, United Kingdom.
Email: j.g.esler@damtp.cam.ac.uk
