An Analysis of a Barotropically Unstable, High–Rossby Number Vortex in Shear

The interactions of the barotropic instability found at low levels in tropical cyclones and a shear forcing are presented. Previous works have indicated that at low levels of tropical cyclones, the inner edge of the core may be barotropically unstable and thereby able to support counterpropagating vortex Rossby wave interactions. It has also been demonstrated that hurricanes and other barotropic vortices possess innate, dry abilities to maintain themselves when under the duress of vertical wind shear. This work will address how these two separate processes interact with each other. In this study, the barotropic ring is given additional vorticity in the outer regions to mimic observations more closely. This allows for the outward propagation of energy and simultaneous reduction of the radius of maximum wind. When this vortex is sheared, it is found that the shear forcing, which acts as a de facto wavenumber-1 forcing, does not noticeably alter the growth of the most unstable mode, wavenumber 3. The tilt precession of the vortex is altered greatly, as the tilt becomes both larger and slower. Palinstrophy and deformation analysis indicates that overall peak mixing is also reduced, owing to changes in the axisymmetrization process. Energetics analyses show that the radial component of the shear forcing acts to generate eddies while the tangential component of the shear tends to destroy eddies. The calculations are carried out a second time with another center-finding method, which shows the tilt to be much smaller and more variable while imparting a large wavenumber-1 signal in Fourier analyses.