Nearly symmetric and nearly baroclinic instabilities in the presence of diffusivity. Part 2. Mode structures and energetics

Abstract

The structures and energetics of nearly symmetric modes and nearly baroclinic modes are analysed in detail to examine their instability mechanisms. It is shown that the nearly symmetric modes have their cross-band circulations slanted mainly between the along-band absolute-momentum surface and buoyancy surface of the basic state. Their growth is thus supported mainly by the symmetric-type energy conversion that transports energy from the basic-state along-band velocity and buoyancy to the perturbation along-band velocity and buoyancy, respectively, and then to the cross-band circulation. However, as the band orientations are tilted slightly away from the basic shear, the growth is also assisted by the baroclinic-type energy conversion that transports energy from the basic-state buoyancy to the perturbation buoyancy via the along-band advection and then to the cross-band circulation. When the band orientation is tilted to the warm (or cold) side of the basic shear, the baroclinic-type energy conversion smooths (or sharpens) the near-boundary structures and thus reduces (enhances) the effect of diffusive damping, especially near the non-slip boundaries. This explains why in the presence of diffusivity the symmetric instability yields to the nearly symmetric instability with the band orientation tilted slightly to the warm side of the basic shear. The nearly baroclinic modes transport warm air northward with rising motion and cold air southward with sinking motion, so their growth is supported mainly by the baroclinic-type energy conversion. Since the band orientations are not exactly perpendicular to the basic shear, the growth is also assisted by two additional energy conversions: (i) from the basic-state buoyancy through the cross-band horizontal advection to the perturbation buoyancy; and (ii) from the basic-state along-band velocity to the perturbation along-band velocity. When the band orientation is tilted, by nearly 90$^\circ$ or less, to the warm (or cold) side of the basic shear, the two additional energy conversions smooth (or sharpen) the near-boundary structures and thus reduce (enhance) the effect of diffusive damping, especially near the non-slip boundaries. This explains why the baroclinic instability yields to the warm-side tilted nearly baroclinic instability in the presence of diffusivity.