The eye of a tropical cyclone – some experiments with an axisymmetric numerical model

Wolfgang Ulrich

New title:

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

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)

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).

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).

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).

Composite hurricane structure (Stull).

Eye: 0...0.5 R

0

Eyewall: (0.5...1) R

0

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.

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

Numerical diffusion in the eye region:

“v” analytic, “p” from gradientwind balance“vnum” from analytic “p” with finite differences.

Animation of a standard case

Relative humidity

Potential Temperature deviation

Moist static energy

Standard case

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

What can limit the contraction ?

Diffusionsubsidence in the eye=> u > 0

No advection of u and v

Colder SST=25 CSST=28 C

2*Eye

P

10 deg

30 deg

40 deg

SST drop after 96 h to 20 C in a ring

GP 0-5

GP 5-10

eye pressure

Thanks to Robert

END