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

Abstract

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. The valve-like critical 'level' absorption (Grimshaw, 1975) is explained by an anisotropic wavefront revolution due to the baroclinicity of the basic field. The induced zonal-mean field, correct to the second order of wave amplitude, resembles an inertial oscillation or a symmetric isopycnical motion. The net absorption rate of the critical 'layer', which coincides with that of the non-inertial waves (Booker and Bretherton, 1967), can be explained by a resonant energy conversion from the wave to the zonal-mean inertial oscillation.The geostrophic flow deceleration results from a kind of resonant redistribution of mean kinetic energy so as to maintain the zonal-mean isopycnical motion; this leads to a final equilibrium state in which Richardson number of the mean zonal flow in the critical layer is unity. Although the non-inertial approximation holds outside the layer with a basic Richardson number larger than unity, above-mentioned features are important to discuss the gravity-wave stress and quasi-horizontal diffusion in the stratosphere.

Gravity Waves Generated by Sheared Three-Dimensional Potential Vorticity Anomalies

“…The configuration that we analyse is quite different since the GW associated with a PV disturbance is generated between the critical levels and propagates outwards of them. Nevertheless, the argument of Yamanaka (1985) applies and we find strong absorption at the inertial level if νΛ > 0 and much weaker absorption if νΛ < 0.…”

“…Even though in both scenarios the initial upward GW is ultimately absorbed at the lowest inertial level, this potential intrusion of the GW signal between the inertial levels is quite remarkable and was referred to as a"valve" effect by these authors. This effect was interpreted heuristically by Yamanaka (1985), who analysed with detail the behaviour of two independent solutions near the lowest inertial level. He pointed out that the phase lines of one of the solutions change direction rapidly around the inertial level, and lie between the horizontal plane and the isentropes in a narrow region.…”

“…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. of particle displacements) relative to the isentropes.…”

Ageostrophic instability in rotating, stratified interior vertical shear flows

“…The inertia critical layer is defined to be where kU(z) − ω = ±f dimensionally, or kU(z) − ω = ±1/Ro non-dimensionally. The physical characteristics of ICL have been recognized as an 'absorber' of inertia-gravity waves (Jones 1967), and Yamanaka (1985) shows that inertia-gravity waves in an ICL can be unstable due to a non-uniform mean flow. We categorize these modes as another type of ageostrophic instability: AI2.…”