1. Scott A. Braun, 2002: Mon. Wea. Rev.,130, 1573-1592.
A Cloud-Resolving Simulation of Hurricane Bob (1991): Storm Structure and Eyewall Buoyancy
Scott A. Braun, 2002: Mon. Wea. Rev.,130,
2004/08/31

2. Introduction
Gray and Shea (1973) remarked that assumption of a relative humidity of 100% in the eyewall leads to small vertical gradients of equivalent potential temperature and little diagnosed potential instability.
Emanuel (1986) suggested that the hurricane eyewall is often close to a state of moist slantwise neutrality in which the and angular momentum surfaces are nearly parallel. This result implies that boundary layer air is neutrally buoyant when lifted along surfaces of constant angular momentum.
Emanuel (1986) and Zhang et al. (2000) suggest that eyewall updrafts are generally neutrally or even negatively buoyant. However, observations of updrafts with in eyewalls show occasionally strong small-scale updrafts (Jorgensen et al. 1985; Black et al. 1994); Heyms-field et al. 2001).
This study uses 2-min output from a 1.3-km grid-scale simulation of Hurricane Bob (1991) to examine the characteristics of the updrafts and buoyancy field within the eyewall.

3. Simulation description and analysis methods
PSU-NCAR MM5 Model
Simulation time: 1991/08/16_0000~1991/08/19_0000 UTC (72 hrs) Domain designed: 36-km (193×163×27) 0~72 hrs, grid fixed, km (163×178×27) 48~72 hrs, grid fixed, km (163×178×27) 48~72 hrs, grid moved, km (163×178×27) 48~72 hrs, grid moved. Cumulus parameterization scheme: Betts-Miller cumulus scheme is used on the 12-km grid, but is not used on 4- and 1.3-km. Cloud microphysics scheme: Goddard cumulus ensemble scheme. Boundary layer parameterization: Burk-Thompson scheme. Cloud radiation scheme: Dudhia (1989) cloud radiation scheme.

4. 4-km grid
low level
upper level
Us, Vs: the zonal and meridional component of the storm motion (averaged the horizontal wind components within 200 km of storm center). UE, VE: the vertically integrated environmental steering flow (900 to 150 hPa of the density-weighted mean following Liu et al., 1999).

5. Kinematic and reflectivity structure
a. Time-averaged structure
rain mixing ratio(h=42m)
tangential velocity (h=42m)
the direction of storm motion, the direction of the surface to 8-km wind shear vector.
1.5-km level vertical velocity with contours drawn at 1( )and 2( )ms-1.
radial velocity (h=42m)
radial velocity (h=1.5km)
inflow outflow

6. wavenumber-1 wavenumber-2
the direction of storm motion, the direction of the surface to 8-km wind shear vector.
the band of wavenumber-0 inflow greater than 20 ms-1.

7. b. Instantaneous low-level horizontal structure
Simulated radar reflectivity patterns at 1 km MSL (mean sea level). Solid lines in (c) show the locations of radial cross sections.

8. At 66 h
inflow outflow
h = 125 m (WN2)

9. c. Vertical structure Vertical velocity & Reflectivity
Radial velocity & Reflectivity

10. d. Vertical mass flux statistics (at 5.2 km MSL)
The cumulative percentage of the eyewall area occupied by vertical velocities less than the magnitude given on the abscissa. The cumulative percentage of the upward mass flux coming from updrafts less than the indicated value. The percentage of the upward mass flux associated with updrafts falling within 0.5 ms-1 bins centered on the indicated values of vertical velocity. cumulative percentages of upward mass flux at 4.5 km; cumulative percentages of upward mass flux at 5.5 km
+ ◇

11. Thermodynamics structure
a. structure
stratiform
contour >345 K >355 K reflectivity contours (15, 30, 45dBZ)
>1 ms >4 ms-1 (vertical velocity) 1 ~ 4 are trajectory locations.
66 h

12. b. Buoyancy in the eyewall
trajectory 3
trajectory 4

13. The total buoyancy (Houze 1993) is defined as WN2 at 66 h (h = 3.2 km)
is virtual potential temperature, is obtained by averaging 1.3-km domain, WN0 and WN1 of the perturbations from
The total buoyancy (Houze 1993) is defined as
WN2 at 66 h (h = 3.2 km)
κ= p is pressure, q’p is the perturbation hydrometeor mixing ratio
starting at 0.5 K, and 1K interval
>1 ms >3 ms-1 (vertical velocity)

14. >1 ms-1 >6 ms-1 (vertical velocity)

15. Following trajectory 3
EL(equilibrium level) at 11.2 km
LFC(level of free convection)at 1.4 km
between 8.5 and 10.5 km: 1. the coarser vertical resolution at these levels, which may cause increased errors in the calculation of the vertical pressure gradient; 2. The fact that the vertical force balance is an instantaneous value while is determined over 2-min intervals.

16. (equivalent potential temperature) absolute angular moment a hypothetical air parcel trajectory in the radius-height plane; the area of the azimuthal mean eyewall updraft.

17. Conclusions
The fact that the majority of the upward mass flux occurs in small-scale updraft cores (wavenumber-0 and-1) suggests that buoyancy plays an important role in the eyewall dynamics.
Calculated eyewall trajectories possess strong vertical accelerations up to the melting level, above which water loading significantly dampens the accelerations or reverses them until precipitation falls out.
A key source for the eyewall buoyancy is the energy gained near the surface by fluxes of moisture and heat from the ocean.
The buoyancy is most often achieved along outward-sloping paths rather than along purely vertical paths.
The low-level vertical motions, inflow, outflow and buoyancy are strongly modulated by a pronounced shaped eyewall.