Transcript Document

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, June 1980, p1227
Force balance in a hurricane
Rotation axis
Primary (tangential)
circulation
Lowest pressure in
the centre
pressure
gradient force
r
v
Centrifugal and
Coriolis forces
Gradient wind balance
v2
1 p
 fv 
r
 r
Primary (tangential) circulation
z
Gradient wind balance
v2
1 p
 fv 
r
 r
warm
v(r,z)
Hydrostatic balance

1 p
0
 ,
 z
cool
g(T  To )

To
r
Thermal wind 
 2v
 v g T
f 



 r
 z To r
Eye dynamics
z
Gradient wind balance
v2
1 p
 fv 
r
 r
warm
1 p
0

 z
v(r,z)
p(z, )  p(z,0) 


 p(z,0) 
z


0


0

   v2
   fv   dr  0
z   r

cool
 v2

   fv  dr
 r

r
v

 0,
0
z
z
Some support
Frictionally-driven secondary circulation
Secondary
circulation
Pressure
gradient force
r
v
v
Centrifugal and Coriolis force are reduced by friction
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
Dynamics of vortex spin down
Vertical cross-section
V
t
V

w
0
z

w
0
z
Boundary layer
Level of nondivergence
Buoyancy in a vortex
warm
 Buoyancy
w
0
z
Tv
Tv

Friction layer

w
0
z
Level of nondivergence
Buoyancy  radial (virtual) temperature difference
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

 p(z,0) 
z


0

   v2
   fv   dr  0
z   r

v

 0,
0
z
z
 The adverse pressure gradient drives subsidence –
just enough to satisfy hydrostatic balance
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
z
r
0.5KM
Boundary-layer control
Vgr
vb
w
|v|b
ub
 In a strong vortex wmax occurs close to rmax and then declines.
The importance of the boundary layer
Path to vmax
f = 0.5fo
Path to vmax
Back trajectories from vmax
Path to vmax
f = 2.0fo
f = 1.0fo
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!