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Hurricane Dynamics 101. Roger K. Smith Universit y of M u nich. Topics. Hurricane eye dynamics Repairing Emanuel’s 1986 Hurricane model. Motivation. FAQs HRD website: What is the "eye"? How is it formed and maintained ?.

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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.

A note of caution

  • Vortices are tightly-coupled flows.

  • Cause and effect arguments are dangerous!


Journal of the Atmospheric Sciences dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent , June 1980, p1227


Force balance in a hurricane
Force balance in a hurricane dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

Rotation axis

Lowest pressure in the centre

Primary (tangential)

circulation

pressure gradient force

r

v

Centrifugal and Coriolis forces

Gradient wind balance


Prim ary tangential circulation
Prim dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent ary (tangential) circulation

z

Gradient wind balance

warm

cool

Hydrostatic balance

v(r,z)

r

Thermal wind 


Eye dynamics
Eye dynamics dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

z

Gradient wind balance

warm

cool

v(r,z)

r


Some support dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent


Frictionally driven second ary circulation
Frictionally-driven second dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent ary circulation

Secondary circulation

Pressure gradient force

r

v

v

Centrifugal and Coriolis force are reduced by friction


Dynamics of spin up
Dynamics of spin up dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

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


Dynamics of vortex spin down
Dynamics of vortex spin down dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

Vertical cross-section

V

Boundary layer

Level of nondivergence


Buoyancy in a vortex
Buoyancy in a vortex dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

 Buoyancy

warm

Tv

Tv

Friction layer

Level of nondivergence

Buoyancyradial (virtual) temperature difference


Why an eye? dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

  • 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


Why not ascent along the axis? dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

  • 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 =>.


dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent


Secondary circulation in dust devil simulations dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

Control => 

2

0.5KM

z

r


Boundary-layer control dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

Vgr

w

|v|b

vb

ub

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


The importance of the boundary layer dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

Path to vmax f = 0.5fo

Path to vmax f = 1.0fo

Back trajectories from vmax

Path to vmax f = 2.0fo


Conclusions dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent

  • 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 dynamically forced centrifuging of mass out of the eye into the eyewall and to a forced descent for your Attention!


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