"Why must hurricanes have eyes?" ? revisited

Abstract

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...

Eye formation in rotating convection

“…That is, axial gradients in Γ can act as a local source of azimuthal vorticity, and indeed this mechanism has been invoked by previous authors in the context of tropical cyclones (e.g. Pearce 2005a;Smith 2005;Pearce 2005b). The idea is that, in steady state, if viscous diffusion is ignored in the vicinity of the eyewall, (4.1) and (4.2) locally reduce to…”

“…One of the most striking features of atmospheric vortices, such as tropical cyclones, is that they often develop a so-called eye; a region of reversed flow in and around the axis of the vortex. Much has been written about eye formation, particularly in the context of tropical cyclones, but the key dynamical processes are still poorly understood (Pearce 2005a;Smith 2005;Pearce 2005b). Naturally occurring vortices in the atmosphere are, of course, complicated objects, whose overall dynamics can be strongly influenced by, for example, planetary rotation, stratification, latent heat release through moist convection, and turbulent diffusion.…”

Formation of eyes in large-scale cyclonic vortices

“…In the case of tropical cyclones, such an eye is readily identified in satellite images by the absence of cloud cover. Despite their common appearance, there is still little agreement as to the mechanisms of eye formation [3][4][5], and indeed it is not even clear that the same basic mechanisms are responsible in different classes of atmospheric vortices [6]. In the absence of such a fundamental understanding, one cannot reliably predict when eyes should, or should not, form.…”

Dynamics of a trapped vortex in rotating convection

“…Though many observations have been made of the nature of the eye in the tropical cyclone, there is still a lack of fundamental understanding as to how or why it forms. A number of different theories have been presented to explain the phenomenon and the topic is still strongly debated -see the exchange of Pearce [6,7] and Smith [8]. Smith [9] suggests that subsiding flow is driven by an axial pressure gradient at the centre of the cyclone imposed by radial pressure gradients due to the swirling flow, a theory that he states complements the ideas of Willoughby [10].…”