Typhoon Dynamics

1. Typhoon Dynamics Roger K. Smith University of Munich Aim To review some of the fundamental processes involved in the dynamics and thermodynamics of typhoon structure and evolution.

2. Outline of talk • Structure of a mature hurricane • Basic dynamics • Primary circulation • The eye • Effects of friction & the secondary circulation • Hurricane intensification • Buoyancy in a hurricane • Maintenance of the warm core • Summary/omissions

3. Schematic cross-section of a mature tropical cyclone Warm core in approximate thermal- wind balance Eyewall clouds: are they buoyant?

4. Structure of a mature hurricane isotachs isotherms Warm core Houze Fig. 10.11 From Wallace and Hobbs, (1977)

5. Primary (tangential) circulation z v(r,z,t)  ~ 500 m Friction layer r

6. Approximate force balance above the friction layer Rotation axis Lowest pressure on the axis Primary (tangential) circulation Radial pressure gradient force Vertical pressure gradient force r Centrifugal force and Coriolis force v Gravitational force Gradient wind balance Hydrostatic balance

7. Thermal wind equation Gradient wind balance Hydrostatic balance Write Eliminate p using Thermal wind equation

8. Physical interpretation Thermal wind equation Balance in toroidal circulation tendency z light heavy z z  light heavy  r r r

9. Mathematical solution Characteristics z z(r) r Governs the variation of ρ along characteristics

10. Characteristics are isobaric surfaces z p = constant po ,ro z(r) r Along a characteristic

11. Inferences p = constant z po ,ro z(r) r Barotropic vortex Baroclinic vortex Equation of state

12. Summary • A barotropic vortex is cold cored if temperature contrasts are measured at constant height. • A baroclinic vortex is warm cored if temperature contrasts are measured at constant height and if-∂v/∂zis large enough. A sample calculation =>

13. A sample calculation

14. The Eye

15. Eye dynamics z Gradient wind balance warm cool v(r,z)  r

16. Summary • The decline in the tangential wind speed with height at all radii  there is a reduced upward force acting on air parcels compared with that at large radii (perturbation pressure gradient is downwards). • The air density is less also and there is approximate balance. • Exactly thermal wind balance  there is no net upward force to drive vertical motion – presumably the case in a mature hurricane. • The subsidence near the axis of a hurricane occurs mainly during the intensification stage. • As the tangential circulation intensifies, the density of an air parcel in the eye must be slightly larger than it would be in the exactly balanced state  the air slowly subsides. • When the tangential circulation weakens, the density is slightly less than in the exactly balanced state  the air slowly rises.

17. Hurricane intensification • Basic principle - Conservation of absolute angular momentum: M = rv + r2f/2 r v v = M/r - rf/2 If r decreases, v increases! Spin up requires radial convergence

18. Frictionally-induced secondary circulation Secondary circulation Pressure gradient force r v v Centrifugal force and Coriolis force are reduced by friction

19. Dynamics of vortex spin down Vertikal cross-section   v Friction layer Level of nondivergence

20. “Tea cup” Experiment

21. Vertical velocity at the top of the friction layer Another reason to expect the existence of an eye!

22. Buoyancy in a hurricane  buoyancy warm Tv Tv   Friction layer Level of nondivergence Buoyancyhorizontal gradient of (virtual) Temperature

23. Sea surface fluxes

24. Maintenance of the warm core in a tropical cyclone qe1 qe2 eye v  qeb1 qeb2   Moisture flux  |Vs|(q*(Ts,p) – qb)

25. Summary • Structure of a mature hurricane • Basic dynamics • Primary circulation • The eye • Effects of friction & the secondary circulation • Hurricane intensification • Buoyancy in a hurricane • Maintenance of the warm core (WISHE mechanism) • Omissions: hurricane motion, asymmetric processes, eye-wall replacement cycles

26. Thank you for your attention!