In a recent thought-provoking article, Pearce (2005) poses the question "Why must hurricanes have eyes"? In the article he explains aspects of the inner-core dynamics of a mature hurricane in terms of a simple axisymmetric model in which the eye is non-rotating and less dense than the vortex surrounding it. He describes a calculation in which the eye always has a finite radius at the surface and the inference appears to be that a similar dynamical constraint applies to a mature hurricane. My aim here is to review some of the important issues raised by Prof. Pearce and to present a slightly different view of the inner-core dynamics of a hurricane and an alternative explanation for the hurricane eye. In particular, I will argue that the foregoing calculation is unrealistic in one important respect and show how it can be repaired. Even so, its relevance to the hurricane eye remains unclear.Prof. Pearce makes a commendable attempt to simplify the concepts required to understand the dynamics involved by considering parts of the problem separately. For example he explains q how azimuthal vorticity is produced in a rising thermal; q why the azimuthal wind speed must decrease with height above the surface friction layer; and q how this decrease leads to an azimuthal vorticity tendency that balances the tendency associated with the negative radial temperature gradient observed in a hurricane.He argues that subsidence must occur in the eye so that the radial temperature gradient in the eye can balance the production of azimuthal vorticity by vortex tilting in the eyewall. However there are some misleading aspects of the discussion that I will try to explain below.
An analysis of Pearce's simple modelFirst let me examine the simple model that always predicts the existence of an eye of finite radius at the surface. The model considers two layers of immiscible incompressible fluid with densities ρ -∆ρ and ρ, where ∆ρ > 0. The lighter fluid that represents the eye is at rest while the heavier one representing the surrounding vortex core is rotating. In the model, an expression is derived for the shape of the surface, h(r), separating the eye from the vortex outside it. The assumption is made that Coriolis forces can be neglected, which is not unreasonable for the rapidly rotating inner core of a hurricane. It is shown that with these assumptions, h(r) satisfies the ordinary differential, where v is the azimuthal (tangential) wind speed, r is the radius, g' = g∆ρ/ρ is the reduced gravity and g is the acceleration due to gravity. It is then assumed, for simplicity, that the vortex outside the eye has uniform angular momentum, i.e. the azimuthal wind profile v(r) satisfies rv(r) = V R R, where V R is the wind speed at some radius R. Then the equation for h can be integrated to give], where H = h(∞) is the value of h at large r and r e = V R R/ √(2g'H). It follows that h is zero when r = r e , which is always finite. In other words, the eye region has a finite width at the surface irrespective of the prescribed strength of the an...