The Concept of Wave Overreflection and Its Application to Baroclinic Instability

Abstract

The concept of wave overreflection is reviewed. The physical origin of this effect is discussed as is its relation to hydrodynamic instability. It is noted that the instabilities associated with overreflection are likely to be identical to what are commonly called critical layer instabilities. The bulk of this paper examines baroclinic instability in terms of the overreflection of vertically propagating Rossby waves. This approach leads to rapid estimates of growth rates and phase speeds of unstable modes for arbitrary distributions of zonal velocities in models with and without lids; it also leads to efficient algorithms for calculating unstable modes “exactly.” Among our findings are the following: (i) Charney and Green modes are both essentially critical-layer instabilities. (ii) When tropospheric shear is brought to zero above some height (one scale height, for example) so that long waves may radiate to infinity (ignoring for a moment the growth rate), the growth rates are reduced somewhat, but the modes remain unstable. (iii) Baroclinic instability can be eliminated by stretching the transition region from zero shear at the ground to the interior shear sufficiently without altering the shear above this region. Explicit calculations show this depth to be about a quarter of a scale height. Consistent with item (iii) above, we show that the potential vorticity flux of baroclinically unstable modes (a measure of their interaction with the mean flow) is confined primarily to a layer between the ground and the neighborhood of the steering level—even when the unstable eigenmodes extend to much greater heights.