hurricane dynamics 101 roger k. smith university of munich

Hurricane Dynamics 101

Roger K. Smith

University of Munich

Topics

Hurricane eye dynamics

Repairing Emanuel’s 1986 Hurricane model

Motivation

FAQs HRD website:

What is the "eye"? How is it formed and maintained ?

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.

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.

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.

Vortices are tightly-coupled flows.

Cause and effect arguments are dangerous!

A note of caution

Journal of the Atmospheric Sciences, June 1980, p1227

v

Lowest pressure in the centre

Rotation axis

pressure gradient force

Centrifugal and Coriolis forces

2v 1 pfv

r r

Gradient wind balance

Primary (tangential)circulation

Force balance in a hurricane

r

Primary (tangential) circulation

warm

v(r,z)

Gradient wind balance2v 1 p

fvr r

Hydrostatic balance

o

o

1 p g(T T )0 ,

z T

o

2v v g Tf

r z T r

Thermal wind

z

r

cool

Eye dynamics

warm

v(r,z)

Gradient wind balance2v 1 p

fvr r

z

r

2

0

vp (z, ) p (z,0) fv dr

r

2

0

vp (z,0) fv dr 0

z z r

1 p0

z

cool

v0, 0

z z

Some support

r

v

Pressure gradient force

Centrifugal and Coriolis force are reduced by friction

v

Secondary circulation

Frictionally-driven secondary circulation

Basic principle:

r

v

v = M/r rf/2 When r decreases, v increases!

Spin up needs radial convergence

- conservation of absolute angular momentum: M = rv + r2f/2

Dynamics of spin up

w

z0

w

z0

Boundary layer Level of nondivergence

V

Vertical cross-section

Dynamics of vortex spin down

V

t

w

z0

w

z0

Friction layer

Buoyancy radial (virtual) temperature difference

Buoyancy in a vortex

Level of nondivergence

warm Buoyancy

Tv Tv

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

2

0

vp (z,0) fv dr 0

z z r

v0, 0

z z

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 =>.

Secondary circulation in dust devil simulations

Control => 2 0.5KM

z

r

Boundary-layer control

Vgr

vb

ub

|v|bw

In a strong vortex wmax occurs close to rmax and then declines.

Path to vmax f = 0.5fo

The importance of the boundary layer

Path to vmax f = 1.0fo

Path to vmax f = 2.0fo

Back trajectories from vmax

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).

Thank you for your Attention!