The Three‐Dimensional Nature of ‘Symmetric’ Instability

Abstract

AbstractThe importance of three‐dimensional effects in a flow with negative potential vorticity is considered here; this is the three‐dimensional counterpart of symmetric instability. the term symmetric instability refers to a two‐dimensional flow with negative potential vorticity which develops roll circulations aligned along the thermal wind. the requirement for exact two‐dimensionality is here relaxed by using three‐dimensional numerical simulations. Two classes of simulation are described; both take a two‐dimensional basic flow.In the first part we explore the response of a flow with uniform negative potential vorticity to localized initial perturbations. It is found that circulations become established which elongate at an angle to the thermal wind. This angle, it is shown, is determined by viscous effects and is in accord with the structure of linear viscous tilted modes for this flow. If, as happens on occasions, such an angle formed by rainbands to the thermal wind is observed in nature, it gives an indication of the importance of viscous effects. In the cases presented here the orientation is such that the rolls tilt towards the warm air as viewed in the direction of the thermal wind; i.e. they are rotated anticyclonically relative to the front. It is shown that these structures, when at finite amplitude, are stable to perturbations imposed along their length.In the second part localized regions of instability are produced which are confined along the thermal wind direction by prescribing in these zones a reduced static stability for vertical motion. This represents the effects of latent‐heat release and it is only in these zones that the effective potential vorticity is negative. It is found that if the length of the zone along the thermal wind direction is smaller than about twice the roll wavelength across that direction then the growth rate is substantially reduced; otherwise it is relatively unaffected by this confinement. It therefore appears that a flow with negative potential vorticity is not only unstable in the pathological two‐dimensional case.