Symmetrization of lopsided vorticity monopoles and offset hurricane eyes

This paper is a contribution towards better understanding of the continually occurring symmetrization processes in tropical cyclones. Before a tropical cyclone develops an eye, it can often possess an asymmetric monopolar vorticity distribution. As an idealized initial condition in a non‐divergent barotropic model, we use a lopsided monopole with different degrees of asymmetry of the monotonic vorticity field. We then study the axi‐symmetrization process which involves the ejection of a winding spiral band. For extreme asymmetric initial conditions, the band can produce regions of barotropic instability, resulting in nonlinear mixing of vorticity and the formation of polygonal structures. In a second series of experiments, we study the case of a tropical cyclone with a developed eye, modelled as a hollow‐tower vorticity distribution, i.e. an annular region of elevated vorticity, with low vorticity in the eye. If the eye is offset and the annular region of elevated vorticity is not of uniform width, complex symmetrization processes can occur, sometimes leading to a tripole structure of the hurricane's vorticity field. Long‐lived hurricane eyes are found for initial conditions with a slight offset. For such initial conditions, passive tracers can remain in the eye for as long as 72 hours, showing that in this model it is possible for air inside the eye to remain there for long periods of time, while moving coherently with the storm. Predictions of the axi‐symmetric final equilibrium states of the flow are obtained using the statistical mechanics theory of maximum Boltzmann mixing entropy. These predictions are then compared with results from the direct numerical integrations for both the lopsided monopole and the offset hurricane eye. The distribution of air‐parcel tracers initially placed in selective regions of vorticity for the direct numerical integrations are compared with results from the statistical theory.