1. Factors Controlling the Intensity of Idealized Hurricanes in Numerical Models*
Richard Rotunno
NCAR
*Based on:
Bryan, G. H., and R. Rotunno, 2008: The influence of near-surface, high-entropy air in hurricane eyes on maximum hurricane intensity. The Journal of the Atmospheric Sciences, in press.
Bryan, G. H., and R. Rotunno, 2008: The maximum intensity of tropical cyclones in axisymmetric numerical model simulations. Submitted to Monthly Weather Review.
Rotunno, R., Y. Chen, W. Wang, C. Davis, J. Dudhia and G. J. Holland, 2008: Resolved turbulence in a three-dimensional model of an idealized tropicaI cyclone. Submitted to Geophysical Research Letters.

2. Hurricane is a heat engine it depends on the temperature of the heat reservoir and the heat sink; the transfer of
Heat to the hurricane and the drag of the ocean on the hurricane wind enter as a ratio; finally the relative humidity of
The air below the lowest clouds is a factor (if RH=1 the air would be saturated and there could be no evaporative heat transfer).

3. Tangential Velocity from an Axisymmetric Numerical Model
Bryan and Rotunno (2008 MWR)

4. Rotunno and Emanuel 1987 (RE87) /
Axisymmetric Numerical Model
Vortex Amplifies under Moist-Neutral Conditions
Steady State Intensity Agrees with Theory (E-PI)
Bryan and Rotunno (2008 MWR)

5. Persing and Montgomery (2003, JAS) using RE87 Model:
Vmax Sensitive to Grid Resolution
7.5 15
Bryan and Rotunno (2008 MWR):
RE87 paper
RE87 code
Vmax Sensitive to
7.5 15

6. Numerical Model
Axisymmetric version of Bryan and Fritsch (2002, MWR) cloud model
Uses newly developed, more accurate numerical techniques
(compared to the RE87 model)
Governing equations conserve mass and energy for saturated flows
Includes dissipative heating
Following RE87, new simulations use SST = 26C, moist-neutral initial sounding, same grid-staggering, simple microphysics, sea-surface transfer, and domain
. New simulations at high grid resolution
( RE87 grid resolution )
(PM03 grid resolution )
Bryan and Rotunno (2008 MWR)

7. Numerical Models 3D Axisymmetric Turbulent fluxes represented by
37km
Turbulent fluxes represented by
mixing-length theory
Turbulent fluxes computed, but
high resolution required

8. Sensitivity to Turbulence Length Scales
essentially
inviscid
PM03
RE87
Bryan and Rotunno (2008 MWR)

9. Sensitivity of Wind Speed to Turbulence Mixing Length lh
Bryan and Rotunno (2008 MWR)

10. Evaluation of the “High-Entropy Reservoir”*
shaded: black dot: location of vmax black line: trajectory
default configuration:
no surface fluxes in eye:
*Persing and Montgomery (2003)
Bryan and Rotunno (2008 JAS)

11. Structure of and Angular Momentum
Bryan and Rotunno (2008 MWR)

12. Horizontal Diffusion Weakens Gradients of and
Bryan and Rotunno (2008 MWR)

13. Vmax , E-PI vs
Bryan and Rotunno (2009 in prep)

14. 1. Moist slantwise neutrality 2. PBL Model
Components of E-PI
1. Moist slantwise neutrality
2. PBL Model
3. Gradient-wind and hydrostatic balance
Bryan and Rotunno (2009 in prep)

15. Flow with small horizontal diffusion not in gradient-wind balance
Bryan and Rotunno (2009 in prep)

16. Rotating Flow Above a Stationary Disk*
* Bödewadt (1940) (Schlichting 1968 Boundary Layer Theory); see also Rott and Lewellen 1966 Prog Aero Sci)

17. There are no observations of radial turbulent fluxes in a hurricane
What is ?
There are no observations of radial turbulent fluxes in a hurricane

18. Numerical Models 3D Axisymmetric Turbulent fluxes represented by
37km
Turbulent fluxes represented by
mixing-length theory
Turbulent fluxes computed, but
high resolution required

19. Weather Research and Forecast (WRF) Forecasts
Radar Reflectivity at z=3km
WRF
ELDORA
Davis et al. (2008 MWR)

20. Domain Idealized TC: WRF Model Physics: f-plane zero env wind
6075km
Idealized TC:
f-plane
zero env wind
fixed SST
Nested Grids
1500km
WRF Model Physics:
WSM3 simple ice
No radiation
Relax to initial temp.
Cd (Donelan)
Ce (Carlson-Boland)
Ce/Cd ~ 0.65
YSU PBL
LES PBL
1000km
111km
333km
37km
Check the vertical grid spacing!
50 vertical levels
Dz=60m~1km
Ztop=27km
Rotunno et al. (2008 GRL)

21. Initial Condition (after RE87)
Axisymmetric initial vortex
Initial sounding WRF neutral
Rotunno et al. (2008 GRL)

22. Instantaneous Maximum 10-m Wind Speed
NOTE: Red to green: shift from PBL to TKE
Rotunno et al. (2008 GRL)

23. 10-m Wind Speed t=9.75d y[km] y[km] max=61.5 max=86.7 max=86.2
Rotunno et al. (2008 GRL)

24. 10-m Wind Speed instantaneous 1-min average Max=85.5 Max=82.3 Max=83.7
37km
37 km
Rotunno et al. (2008 GRL)

25. 10-m Tangentially Averaged Wind Speed vs Grid Interval
Rotunno et al. (2008 GRL)

26. Eddy Kinetic Energy Spectra
Change x-axis ticks to 1/meter
Change color to be consistent
KE on a circle with max ke_mean
Rotunno et al. (2008 GRL)

27. grid-scale waves & turbulence
Estimation of Eddy Viscosity for Axisymmetric Models
LES
grid-scale
grid-scale
subgrid-scale
TC Vortex
grid-scale
azimuthal average
grid-scale waves & turbulence

28. Conclusions
Treatment of turbulence in numerical models of hurricanes is as important for intensity prediction as other factors (e.g. sea-surface transfer, ocean-wave drag, cloud physics…)
Quantitative information needed on turbulent transfer in hurricanes
Observations are expensive, LES so far inconclusive