Interaction of Tropical Cyclones
with th
he Upper Ocean
• Resonance with near-inertial
oscillations
ill ti
• Mixed layer cooling by entrainment
• Coupled models
1
Change on SST needed to cancel increase in enthalpy in
core:
Lv q *(Ta )H  c pTa  Lv q *(Ta  T )  c p (Ta  T )
q *
Lv q *(Ta  T )  Lv q *(Ta )  Lv
T
T
Lv q *
 Lv q *(Ta )  Lv
T
2
RvTa
Lv q * 1  H 
o
 T 

2.5
C
2
Lv q *
cp 
2
RvTa
2
Physics of nearnear-inertial oscillations:
PEs linearized about a rotating stratified fluid at rest:
u
pp
  0
 fv
t
x
v
pp
  0
 fu
t
y
w
w
p
  0
B
t
z
B
B
2
 N w
t
uu v w
 
0
x y z
3

2
2 2
2  w
 2 3 w  N  2 w  f
0
2
t
z
2
2
w  w0 e

i  kx  ly  rz t 
2
2
r
 N 2 2 f 2 2,
 r
 r
2
2
2
  k l
2
  f
2
2
2
2
2
N 2
r  2 
f
2
for
4
5
Mixing
g and Entrainment:
6
Entrainment Formulation:
Criticality of a Bulk Richardson Number:
gh
gh
Ri 
2
u
Assume that density jump is what would result from eroding a
constant background stratification down to depth h :
1 h2 N 2
Ri 
2 u2
Equivalently,
Nh  R ' u
(1)
R '  2 Ri
7
Criticality assumption: R’ = constant.
Mixed layer momentum conservation (neglecting
Coriolis turning) :
   wuh 
  a u*2 .
t
((2))
u*2  CD | V |2
Combine (2) with (1):
 a u*2
h 2
 R'
tt
w N
8
Note: units of
diffusivity
Comparison with same atmospheric model coupled to 3-D ocean
model; idealized runs:
F ll mod
Full
dell (bl
(black),
k) sttring
i mod
dell ((red)
d)
Courtesy of Robert Korty. Used with permission.
9
Mixed layer depth and currents
Courtesy of Robert Korty. Used with permission.
10
Courtesy of Robert Korty. Used with permission.
11
SST Change
Courtesy of Robert Korty. Used with permission.
12
Courtesy of Robert Korty. Used with permission.
13
Courtesy of Robert Korty. Used with permission.
14
Define feedback factor:
FSST
p


1,
p |SST
where p |SST is the central pressure drop at fixed SST. Do
many many numerical expreiments
many,
expreiments, varying SST
SST, Coriolis
parameter, traslantion speed, etc. Curve fit dependence
of FSST on these parameters. Result:
15
16
FSST  0.87e  z
1.04
 h0 
z  0.55
0 55 

 30 m 

0.85
 uT 

1 
 6ms 


f

5 1 
 5 10 s 
0.97
0.59
 p
p |SST 


 50 hPa 
0.78





2
1 
 8 10 K m 
η= storm size scaling factor
17
0.40
0.40
 1 H 


 0.2 
00.46
46
18
Effects of Environmental Wind
Shea
Shearr
• Dynamical effects
• Thermodynami
Th
d
ic effects
ff
• Net effect on intensity
19
20
21
PV dynamics
22
Streamlines (dashed) and θ surfaces (solid)
23
24
25
This image has been removed due to copyright restrictions.
Secondary circulation of a idealized TC (a), along with the legs of the
secondary circulation represented on a entropy-temperature diagram (b). TC without
ventilation travels along A-B-C-D, while a ventilated TC travels along A-B′-C′-D. Hatched
region in (b) denotes the work lost due to ventilation. From Tang(2010)
26
This image has been removed due to copyright restrictions.
Normalized equilibrium solutions (solid and dashed lines) for the
steady state intensity of a ventilated TC
TC. Arrows denote intensifying
and weakening TCs for off-equilibrium values of intensity and
ventilation. From Tang (2010).
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This image has been removed due to copyright restrictions.
(a) Jul
Jul.-Oct
-Oct. ventilation index for the Northern Hemisphere and (b) Dec
Dec.-Mar
-Mar.
ventilation index for the Southern Hemisphere averaged over 1981-2000.
Results are shown as the log10(VI). From Tang (2010).
28
This image has been removed due to copyright restrictions.
Percentag
ge of dayys with a VI below 0.1 for (a)) the Northern Hemisp
phere TC
season and (b) the Southern Hemisphere TC season during 1981-2000
(shaded with contours every 10%). TC genesis points for the same period
are denoted by black dots. From Tang (2010).
29
This image has been removed due to copyright restrictions.
Grayscale shading indicates the number of daily TC observations in the
MGR as a function of the VI and normalized intensity, i.e. the intensity divided by
the potential intensity.
intensity Arrows signify the mean 24 hour normalized intensity change
for TCs in each bin with green and red arrows indicating normalized strengthening
and weakening, respectively. The maximum arrow length corresponds to a
normalized intensity change of 0.4 over 24 hours. From Tang (2010).
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Model
(Rappin,
pp ,2010
)
WRF V2.2.1
Doublyy periodic domain
Fixed SST
3 km horizontal resolution
40 vertical levels (stretched in height)
YSU PBL scheme
 Improved
I
d drag
d
formulation
f
l ti (Donelan
(D
l ett al.
l 2004
2004; D
Davis
i
et al. 2008)
 WRF 6
6-species
species microphysics scheme
 RRTM longwave scheme
 Goddard shortwave with perpetual equinox





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Methodology
1. Fix SST, vertical shear, Coriolis parameter, and mean
surface wind.
2. Run a small domain (150 km x 150 km) simulation with
random low-level thermal perturbations to radiativeconvective equilibrium (90 days)
days).
3. Calculate RCE thermodyynamic sounding
gs and wind
profiles. Calculate large scale quantities (i.e. MPI,
CAPE, χ…).
4. Use RCE data to initialize large domain (1200 km x
1200 km) simulation of tropical cyclogenesis from a
mid-level
mid
level vortex modeled after easterly waves
waves.
32
Initial Condition
33
Vertical Shear
How do we incorporate shear into a doubly periodic domain?
1. Initialize domain with RCE wind profile U(z).
2. Add a term to the press
pressure
re gradient that balances U(
U(z):
)
Dv

 fu  
 fU (z)
yy
Dt
34
35
Experiment Control (Developing): WVP (colorfill), surface wind vectors, and 550 hPa
geopotential height Wavenumber 1
asymmetry
Surface divergence
beneath mid-level vortex
36
Experiment Control (Developing): WVP (colorfill), surface wind vectors, and 550 hPa geopotential
height Zonal line of convection develops where the primary flow impinges upon the surface divergence field. An MCS!
37
Experiment Control (Developing): WVP (colorfill), surface wind vectors, and 550 hPa geopotential height Sustained
S
stained con
convergence
ergence on
down-shear left flank results
in height falls due to vortex
tube stretching.
38
Experiment Control (Developing):
WVP (colorfill), surface wind vectors, and 550 hPa geopotential height 39
Experiment WARM (non‐developing) :
WVP, surface wind vectors, and 550 hPa geopotential height.
40
Experiment WIND (non‐developing): WVP(colorfill), surface wind vectors, and 550 hPa geopotential height. 41
Control: Meridionally averaged column integrated saturation deficit Rapid Intensification (mesoscale saturation)
Genesis Proxy
Development and inward precession of new mid‐level vortex
p
Propagation of the original mid‐level
id l l vortex
t
42
Control: Meridionally averaged column integrated saturation deficit and surface fluxes Rapid intensification
Genesis proxy
Mid‐level vortex formation
Surface fluxes due to thermodynamic disequilibrium
Surface fluxes due to convective gustiness
43
Control: Meridionally averaged column integrated saturation deficit, surface fluxes, and dry static energy Column integrated dry static energy controlled by column integrated temperature
Post-saturation – Boundary layer warms by surface
fl
fluxes.
Convection
C
ti carries
i moist
i t static
t ti energy aloft.
l ft
Column warming results in hydrostatic pressure falls.
Pre-saturation – Diabatic heating offset by adiabatic
fluxes off
ffset by convectiive
cooliling. Warmiing by surfface fl
downdrafts.
44
WARM: Meridionally averaged column integrated saturation deficit and surface fluxes No sustained localized convection due to convective downdrafts
No mid‐level vortex!
Very large column integrated satturati
tion deficit
d fi it in the
th core
Downdrafts!
45
MIT OpenCourseWare
http://ocw.mit.edu
12.811 Tropical Meteorology
Spring 2011
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