Propagation and Breakdown of Internal Inertio-Gravity Waves Near Critical Levels in the Middle Atmosphere

Abstract

Behaviors of internal inertio-gravity waves (IIGW) near Jones' critical levels are studied theoretically in view of a possible origin of turbulence layers in the middle atmosphere. The inertial effect associated with the earth's rotation cannot be neglected when time constant of the wave is large. Assuming that the vertical shear and Coriolis factor are constant, exact solutions of IIGW are obtained from inviscid and linear equations. The asymptotic expressions are derived by means of the Liouville-Green method developed by Olver (1974) which leads to an exact dispersion relation near the critical levels. Two important features about critical level problem of IIGW are found from the dispersion relation: valve effect across the Jones' critical levels in somewhat different sense from Grimshaw (1975, 1980), and presence of a pair of turning levels between both Jones' critical levels. Coupling these features, we predict that IIGW is absorbed or reflected by the Jones' critical levels depending on the direction of wave-front. The absorption rate and the thickness of turbulence layer produced by critical level breakdown increase as the wave-fronts tend to direct to the zonal direction, on the other hand IIGW is substantially reflected when they direct to the meridional direction. With increase of basic Richardson number the turning levels approach asymptotically the critical levels, so that turbulence layers inside the critical levels become thinner than those outside them. These features vanish in the case of non-inertial gravity waves.
The relation between IIGW and turbulence layers is calculated to compare with the turbulence layers observed in the stratosphere and to have information on IIGW's propagating upwards to the mesosphere and the thermosphere. In general, thickness of the turbulence layers associated with IIGW's is thinner than that associated with non-inertial gravity waves for common mesoscale wavelength domain.