Hurricane Eyewall Structures Have Been Observed to Attain Shapes That Divert from Circular

Hurricane eyewall structures have been observed to attain shapes that divert from circular geometry. Complex eye polygonal structures, ranging from triangles to hexagons, have been observed from film recordings of storms like Hurricanes David (1979), Betsy (1965), and several others (Lewis and Hawkins 1982; Muramatsu 1986). It is believed that many of these features can be explained to a high level of confidence in terms of internal vortex dynamics and not so by the large scale steering currents that surround the storm. Schubert et al. (1999) and Kossin and Schubert (2001) linked these distortions to barotropic instability of eyewall flows and the mixing of low potential vorticity (PV) fluid in the eye of the hurricane with the surrounding high PV fluid in the eyewall. Schubert et al. (1999) argued that the number of vertices of the polygonal shapes was a function of the wavenumber of maximum dynamic instability of the eyewall flow.

We use an unforced nondivergent 2D barotropic model in order to study the nonlinear evolution of hurricane eyewalls. We consider an idealized framework in which only conservative nonlinear (advective) vorticity dynamics are considered. We initialize our experiments with a barotropically stable annulus of high vorticity and a small region of enhanced vorticity in the eye (see Figure 1 at 0h). Numerical integrations of these initial conditions reveal an axisymmetrization process that results in a variety of polygonal shapes and eyewall contraction. Again, the dynamical aspects of the evolution of the vorticity field in our model are assumed to be highly nonlinear and owed to the horizontal advection of vorticity. The primary role of advective processes, with only a limited amount of diffusion applied, is easily described by looking at the two-dimensional(2D) barotropic nondivergent vorticity equation

(1)

whereis the relative vorticity, ( , )/(x,y) is theJacobian operator, which contains the advective terms, and the diffusion term is the one at the right-hand side of the equation.

Figure 1 shows the vorticity pattern in the annular ring evolving into a square shape at ~56h. At 72h, the 4-sided polygonal shape is still robust with well-defined straight lines and vertices. Figures 2 and 3 show the initial vorticity field and evolution at 44h, respectively, for another experiment. This time we added two regions of enhanced vorticity or mesovortices in the eye. At 44h, a hexagonal eye structure is clearly depicted.

Our goal is to systematically explore how the specific details of these eyewall shape evolutions depend on our initial conditions. We are considering the sensitivity of the evolutionary patterns of the hurricane eye and eyewall regions to the initial values of several parameters: 1) distance of the small region of enhanced vorticity from the center of the model’s domain, 2) radius of the small added vortex, 3) number of added vortices, 4) thickness of the eyewall, 5) intensity of the added vortex, 6) vorticity of the eye region, and 7) vorticity of the eyewall.