Sudden onset of eye occurrence in thermally forced axisymmetric vortices

This paper investigates axisymmetric balanced flow of a stably stratified non-Boussinesq atmosphere on the f-plane. The flow is forced by heating in the vortex center, which is implemented as relaxation towards a specified equilibrium temperature T_e. The flow is dissipated through surface friction, and it is assumed to be almost inviscid in the interior. Previous work has shown that essential vortex properties in this system are controlled by the ratio F = alpha_T / c_D, where alpha_T is the rate of thermal relaxation and c_D quantifies the strength of surface friction for a given surface wind. There is a smooth transition between hurricane-like vortices (which occur in the limit of large F) and monsoon-like vortices (which occur in the limit of small F).

The present contribution focusses on the occurrence, formation and maintenance of an eye, which is defined with reference to the radial profile of the vertical wind. An eye may occurr even though the equilibrium temperature T_e does not predispose any such structure. Key parameter for the existence of an eye turns out be F. The transition between 'no-eye' and 'fully-develped eye' is rather sudden, suggesting strongly nonlinear underlying processes. The point of transition is related to vortex properties like the absolute vorticity and its relation to f. Given T_e, the mechanism for eye-formation in our numerical spin-up integration is essentially inviscid. On the other hand, the maintenance of an eye in steady state relates to Ekman-pumping, which is a viscous process. Implications for eye formation in tropical cyclones will be discussed.