Hurricane Dynamics 101

1. Hurricane Dynamics 101 Roger K. Smith University of Munich

2. Topics • Hurricane eye dynamics • Repairing Emanuel’s 1986 Hurricane model Motivation FAQs HRD website: • What is the "eye"? How is it formed and maintained ?

3. It has been hypothesized (e.g. Gray and Shea 1973, Gray 1991) that supergradient wind flow (i.e. swirling winds that are stronger than what the local pressure gradient can typically support) present near the radius of maximum winds (RMW) causes air to be centrifuged out of the eye into the eyewall, thus accounting for the subsidence in the eye. • However, Willoughby (1990b, 1991) found that the swirling winds within several tropical storms and hurricanes were within 1-4% of gradient balance. • It may be though that the amount of supergradient flow needed to cause such centrifuging of air is only on the order of a couple percent and thus difficult to measure.

4. The general mechanisms by which the eye and eyewall are formed are not fully understood, although observations have shed some light on the problem. • The calm eye of the tropical cyclone shares many qualitative characteristics (?) with other vortical systems such as tornadoes, waterspouts, dust devils and whirlpools. • Given that many of these lack a change of phase of water (i.e. no clouds and diabatic heating involved), it may be that the eye feature is a fundamental component to all rotating fluids.

5. Thus the cloud-free eye may be due to a combination of dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent caused by the moist convection of the eyewall. • This topic is certainly one that can use more research to ascertain which mechanism is primary. A note of caution • Vortices are tightly-coupled flows. • Cause and effect arguments are dangerous!

6. Journal of the Atmospheric Sciences, June 1980, p1227

7. Force balance in a hurricane Rotation axis Lowest pressure in the centre Primary (tangential) circulation pressure gradient force r v Centrifugal and Coriolis forces Gradient wind balance

8. Primary (tangential) circulation z Gradient wind balance warm cool Hydrostatic balance v(r,z)  r Thermal wind 

9. Eye dynamics z Gradient wind balance warm cool v(r,z)  r

10. Some support

11. Frictionally-driven secondary circulation Secondary circulation Pressure gradient force r v v Centrifugal and Coriolis force are reduced by friction

12. Dynamics of spin up Basic principle: - conservation of absolute angular momentum: M = rv + r2f/2 r v v = M/r - rf/2 When r decreases, v increases! Spin up needs radial convergence

13. Dynamics of vortex spin down Vertical cross-section   V Boundary layer Level of nondivergence

14. Buoyancy in a vortex  Buoyancy warm Tv Tv   Friction layer Level of nondivergence Buoyancyradial (virtual) temperature difference

15. Why an eye? • Air that converges at low levels must diverge aloft • When air diverges it spins more slowly and the maximum tangential wind speed occurs at a larger radius • Therefore • The adverse pressure gradient drives subsidence – just enough to satisfy hydrostatic balance

16. Why not ascent along the axis? • In the earlier stages (low rotation), this may happen. • If the core warms up through latent heat release in a few clouds, the buoyancy force near the axis may be larger than the downward pressure gradient force associated with the decay and radial spread of the vortex with height. • As rotation increases, so does the downward axial pressure gradient. • Also as heated region expands radially, the forcing becomes larger near the edge of this region. • Insights from other types of vortices => • Boundary-layer control =>.

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18. Secondary circulation in dust devil simulations Control =>  2 0.5KM z r

19. Boundary-layer control Vgr w |v|b vb ub • In a strong vortex wmax occurs close to rmax and then declines.

20. The importance of the boundary layer Path to vmax f = 0.5fo Path to vmax f = 1.0fo Back trajectories from vmax Path to vmax f = 2.0fo

21. Conclusions • The forced subsidence in the eye is driven by the downward perturbation pressure gradient that arises because the tangential wind field decays and spreads with height. • This pressure gradient is approximately in hydrostatic balance with the buoyancy force in the eye. • The tangential circulation of the vortex decays with height because the flow above the boundary layer is outwards. • The boundary layer of a hurricane-strength vortex exerts a control on where ascent occurs – wmax occurs near rmax. • Azimuthal vorticity generation is a maximum where radial buoyancy gradients are largest. • Mixing in the eye may be important in eye evolution, but doesn’t change the foregoing arguments – it changes v(r,z).

22. Thank you for your Attention!