hurricane dynamics 101 roger k. smith university of munich
TRANSCRIPT
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!