The Theory of the Vertical Propagation of Quasi-Geostrophic Disturbances in the Presence of Distorted Background Flows

Abstract

The structure and vertical propagation of a quasi-geostrophic disturbance in the presence of a constant zonal flow which has been distorted by a finite-amplitude forced stationary wave is considered. The vertical structure of the finite-amplitude wave is given by an eigenvalue of the basic state potential vorticity equation. The disturbance is described by a truncated set of Fourier modes in the east-west direction whose vertical structure is found by solving a second-order Green's function equation. Variations with respect to time are ignored and the usual inviscid, adiabatic assumption is made. It is found that the distortion of the basic flow is manifested, as far as the disturbance is concerned, as a horizontal sheet of horizontal potential transport, and the resulting solution behaves as if a critical level occurred at this level in spite of the fact that the zonally-averaged east-west ambient flow is height-independent. It is shown that heat and energy propagation by a disturbance of central wavenumber 2 can be significantly enhanced by the presence of a wavenumber 1 distortion of ambient westerlies. On the other hand, transports by a disturbance of central wavenumber 1 are normally suppressed and, in fact, can be in the opposite direction to what would be expected with an undistorted zonal flow. These effects on wavenumber 2 agree with the suggestion of Matsuno after his numerical study, which did not account for the distortion of the ambient flow. Also a node-like vertical structure introduced into wavenumber 1 agrees with the observational study by Sato.