The nonlinear evolution and potential vorticity transport of symmetric equatorial inertial instability

The diabatic circulation in the middle atmosphere near solstice transports PV from the summer to winter hemisphere, creating a band of anomalous PV on the winter side of the equator which satisfies the necessary and sufficient conditions for inertial instability. The goal of this presentation is to illustrate the mechanisms through which inertially unstable disturbances stabilize the flow via redistribution of zonal momentum and potential vorticity. The redistribution process is examined in simulations conducted with a nonlinear primitive equation model that fully resolves the inertial disturbances. This resolution was accomplished by giving larger scale disturbances a 'head start', and by employing hyperdiffusion in order to control the development of small scales. It is found that stabilization is accomplished through several mechanisms: 1) the 'quasi-linear' interaction between the disturbance and mean flow that results from the growth of the disturbance; 2) mixing as a result of convective overturning; 3) diffusive decay of small scale disturbances that arise from the self-interaction of the initial disturbance as well as the convective overturning. The diffusive transport of 'PV substance' ultimately results in an up-gradient transport of PV that returns anomalous PV to the summer hemisphere. The evolution of the mean flow is toward a state of constant angular momentum throughout a region that has twice the width of the initially unstable region.

Experiments were also conducted with an imposed mean meridional circulation in an attempt to maintain an inertially unstable flow. It was found that inertial instability was largely ineffective in preventing anomalous PV from being advectively transported across the equator. A surprising discovery was that the meridional circulation itself provided a new type of scale selection mechanism for inertial disturbances. Standard linear theory dictates that the growth rate of the disturbance increases as the vertical scale decreases, implying that a fully developed disturbance will have no preferred scale. However, in these experiments in which no diffusion was imposed, it was found that a preferred vertical length scale developed that was roughly proportional to the strength of the meridional flow. A solution of the governing equations was found using asymptotic methods that verifies this result. An explanation of this new type of scale selection method will be discussed.