![Page 1: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/1.jpg)
The eye of a tropical cyclone – some experiments with an axisymmetric numerical model
Wolfgang Ulrich
New title:
![Page 2: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/2.jpg)
Motivation:
Axisymmetric numerical models of evolving tropical cyclones>>seem<< to >>simulate<< smaller radii of maximum winds(=>eyes) if the resolution is increased.
Examples:DeMaria & Pickle 1988Baik et al 1989NCM, RKS, HYZ and WU 2002WU, RKS and NCM 2002
![Page 3: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/3.jpg)
Idealized anatomy of a tropical cyclone (eye)
At the center of the storm is a cloud-free eye of relatively lowsurface pressure, warm temperature and subsiding air. (Stull)
![Page 4: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/4.jpg)
Observed (eye) characteristic
Hurricane Bonnie from space
Most (but not all) tropical cyclones that reach hurricane intensity have central clear regions, called >>eyes<<; these range in diameter from 20 km to as much as 200 km (Emanuel).
![Page 5: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/5.jpg)
Hurricane Fefa (North Pacific)
Without an eye, tropical storms are limited to a pressureof about 1000 mb .... no matter how much condensation is occuring (Anthes).
![Page 6: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/6.jpg)
Although the basic structure of tropical cyclones is invariant, there is considerable variability in the both the details of the structure and the overall horizontal scale of the storms.
In particular, the characteristic horizontal scale of tropical cyclones varies over a wide range, from “midget typhoons", with eyes only a few kilometers in diameter and with no noticeable wind perturbation outside of 100 km from the storm center, to some “supertyphoons" with eyes up to 200 km in diameter. Thus a midget typhoon can fit entirely within the >>eye<< of a giant supertyphoon!
There is no known correlation, however, between the geometric size of a tropical cyclone and its intensity, as measured, for example, by its maximum wind speed (Emanuel).
![Page 7: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/7.jpg)
Composite hurricane structure (Stull).
Eye: 0...0.5 R
0
Eyewall: (0.5...1) R
0
![Page 8: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/8.jpg)
Axisymmetric finite difference Model
Physics:
●Latent heat release on the grid scale (horizontal 5 km)●Evaporation of falling rain●Sensible heat transfer at the ocean's surface●Bulk friction●Vertical and horizontal exchange based on mixing length●No radiation●No ice●No cummulus parameterization●Hydrostatic Sigma coordinate 15 layers, top at 50 hPa
Numerical methods:
●Adams Bashforth●Flux form 6-th order in r, 3-rd order in Sigma.
![Page 9: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/9.jpg)
Standard run:
Jordan tropical sounding, SST=28 C, 15 deg NorthInitial disturbance 15 m/s (150 km), 12.4 m/s (300 km) 0 (950 km)
Initialisation:balance equation for surface pressureWang (1995) or Kurihara (1974) type initialisation
![Page 10: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/10.jpg)
Numerical diffusion in the eye region:
“v” analytic, “p” from gradientwind balance“vnum” from analytic “p” with finite differences.
![Page 11: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/11.jpg)
Animation of a standard case
![Page 12: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/12.jpg)
Relative humidity
Potential Temperature deviation
![Page 13: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/13.jpg)
Moist static energy
![Page 14: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/14.jpg)
Standard case
![Page 15: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/15.jpg)
Eye contraction, basic mechanism
Assume tangential profile v(r) => radial profile u(r) from balance(f+v/r) u=Friction
Absolute Angular Momentum conservation: AAM=v r + 0.5 f r2
![Page 16: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/16.jpg)
What can limit the contraction ?
Diffusionsubsidence in the eye=> u > 0
![Page 17: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/17.jpg)
No advection of u and v
![Page 18: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/18.jpg)
Colder SST=25 CSST=28 C
2*Eye
P
![Page 19: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/19.jpg)
10 deg
30 deg
40 deg
![Page 20: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/20.jpg)
SST drop after 96 h to 20 C in a ring
GP 0-5
GP 5-10
eye pressure
![Page 21: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/21.jpg)
Thanks to Robert
![Page 22: The eye of a tropical cyclone – some experiments with an axisymmetric numerical model](https://reader035.vdocument.in/reader035/viewer/2022062500/568153b7550346895dc1b98c/html5/thumbnails/22.jpg)
END