Lagrangian Boundaries Separate Developing Cyclones from Dry Environments

Recent theoretical and observation evidence suggests that the presence of a set of flow boundaries in a wave-relative frame provides the necessary protection of developing tropical disturbances from their environment, allowing convection and vorticity aggregation to amplify and concentrate existing cyclonic vorticity. These Eulerian boundaries are not exactly closed as transport across them may occur due to time-dependence or convergence. Lagrangian boundaries offer a more complete description of the permeability of the boundary surrounding the disturbance. By locating and following the evolution of these boundaries, we see more details of the interaction between the disturbance and its environment. We find two possible configurations for Lagrangian transport; an open pathway that allows potentially unlimited dry air to enter, or a semipermeable boundary, in which air contained within lobes, regions bounded by the stable and unstable manifolds of a hyperbolic trajectory, which limits the amount and depth of entrainment. Examples of these configurations are shown for tropical disturbances using ECMWF hi-res data.

As we follow the evolution of these boundaries further, we see that the accumulation of manifolds into a limit cycle forms an additional boundary closer to the cyclone core, a shear sheath that bounds the region of highest rotation. We locate this boundary as the maximum radial gradient of the Okubo-Weiss parameter integrated along particle trajectories. We see that this boundary, once formed, forms a complete barrier around the inner core, and prevents any further transport from occurring, including dry air that would disrupt the cyclone, or mergers which would increase the circulation. Combining these ideas of Lagrangian boundaries for the outer flow and inner core, we see that the question of development versus non-development becomes whether the lateral transport of dry air is sufficiently limited so that a shear sheath can be established.