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. * Graduate student of Nagoya University.

Gravity Waves Generated by Sheared Three-Dimensional Potential Vorticity Anomalies

“…This is a significant limitation since the absorption of GWs at inertial levels strongly depends on the orientation of the horizontal wavevector. This is known from the investigations on GW propagating upward into interial levels: Grimshaw (1975) and Yamanaka and Tanaka (1984) showed that the absorption at the lowest inertial level is large for νΛ < 0, where ν = l/k is the ratio between the transverse and parallel horizontal wavenumbers, and much smaller for νΛ > 0. This results in a 'valve effect' which Yamanaka (1985) interpreted by analyzing the tilt of the phase lines of the GWs (i.e.…”

“…A strong meridional asymmetry in absorption was highlighted by Grimshaw (1975) and Yamanaka and Tanaka (1984) in their studies of GWs propagating upward toward a critical level surrounded by two inertial levels. The latter authors showed that there is a very strong absorption at the lowest inertial level if νΛ < 0.…”

“…Note that W depends on J and ν in addition to ξ, and that we use the notation W (ξ) as a shorthand for the more complete, but more cumbersome W (J, ν; ξ). In Appendix A, we follow Yamanaka and Tanaka (1984), Plougonven et al (2005), and LPV10 and solve this equation exactly using a change of variable that transforms the homogeneous part of (2.13) into the hypergeometric equation. The solution satisfies 14) and 15) corresponding to an upward-(downward-) propagating GW as ξ → +∞ (ξ → −∞).…”

Inertial Oscillation and Symmetric Motion Induced in an Inertio-Gravity Wave Critical Layer

“…An inertio-gravity wave critical layer is defined as the region in which the conventional WKB-type dispersion relation is mathematically invalid (Yamanaka and Tanaka, 1984b). This layer is bounded by a turning level at which wavefront parallels the basic isopycnic surface and by a level inside which geostrophic adjustment for the wave momentum can hardly take place.…”

“…G. W.' is an abbreviation of 'gravity waves'. The other notations of symbols are conventional and defined in the text or in Yamanaka and Tanaka (1984b). Note that f and * are intrinsic frequencies at the critical and turning level, respectively.…”