The latitudinal structure of the quasi-biennial oscillation

The theory of symmetric time-dependent meridional circulations in a radiatively damped atmosphere shows that, when the frequency sigma of the time variation of an applied body force is smaller than the radiative damping rate alpha, there are two distinct forms of response to the force. At high latitudes, the response appears primarily as a quasi-steady meridional circulation, whilst at low latitudes it appears primarily as an acceleration. The transition from 'low-latitude' to 'high-latitude' response occurs at a distance from the equator where N is the buoyancy frequency, D is the depth scale of the force and beta is the horizontal gradient of the Coriolis parameter at the equator. It is argued here that this latitudinal scale may also be that of the quasi-biennial oscillation (QBO), in that the width of the region where there is a substantial QBO in the zonal wind may be determined by the radiative damping rate and the frequency of the oscillation at the equator, rather than by the latitudinal scale of the wave-momentum fluxes (provided that this latter scale is sufficiently broad). Numerical simulations of QBO-like oscillations are carried out in a two-dimensional (height and latitude) model with wave-momentum fluxes imposed independently at each latitude. Variation of the background rotation rate and the thermal damping rate between these simulations helps to elucidate the effect of these two parameters on the latitudinal structure of the oscillations. In particular, it is shown that, provided that there is weak lateral transport of momentum, the width of the oscillation does indeed correspond to the low-latitude/high-latitude transition scale given above. For this mechanism of equatorial confinement, the depth scale D is, in effect, set by the vertical phase variation of the oscillation, which is highly unrealistic in many simple QBO models.