An Air-Sea Interaction Theory for Tropical Cyclones

Part I: Steady-State Maintenance

LIU Yan

-  Emanuel, K.A. (1986) An Air-Sea Interaction Theory for Tropical Cyclones. Part I: Steady-State Maintenance. Journal of Atmospheric Sciences, 43, 585-605.

Conditional Instability VS Air-Sea Interaction

Which is the key process to the development and maintenance of TC?

Conditional Instability VS Air-Sea Interaction

“entirely by the air-sea interaction”

•  Hydrostatic and gradient wind balance (steady-state, cyclone scale)

•  Thermodynamically reversible (constant 𝜽↓𝒆↑∗  , M ǁ 𝜽↓𝒆↑∗ )

•  Neutrality to slantwise moist convection (no ambient CAPE)

An idealized axisymmetric steady-state model of a mature TC

Maxwell’s relations M ǁ 𝜽↓𝒆↑∗ 

Structure above the Boundary Layer

Carnot Heat Engine

∆ Q↓𝟏 

∆ Q↓𝟐 

W↓PBL 

W↓o 

Carnot Heat Engine

Bernoulli’s equations

Work done in outflow

z=h, r=0

z=0

Central Pressure

Central Pressure

Central RH=100% Ambient RH=80%

Temperature Surpluses

How to explain the observed absence of TCs when SST<26℃

Central Pressure

Minimum attainable surface central pressure in September

Central RH=100%

Ambient RH: observation or 78%

•  Region 1：Eye (unsaturated) •  Region 2：Eyewall (saturated) •  Region 3：Constant RH

The Boundary Layer

outer region inner region

Outer region: enhanced evaporation balanced by turbulent flux through BL Inner region: turbulent flux through BL is negligible

The Boundary Layer

inner region outer region

Inner Region

r

Z

Analytical Solutions

outer region

inner region

free atmosphere

•  Free atmosphere

•  Outer region

•  Inner region RMW

r

Z

Analytical Solutions

outer region

inner region

free atmosphere

RMW

Analytical Solutions

V↓max 

R↓o  R↓o 

T↓o 

T↓s 

R↓max  R↓max 

T↓o  T↓s 

Two-dimensional Structure

saturated moist static energy

T

𝝅

𝜽 q∗

r M( 𝛉↓𝐞↑∗ ) :

Z

Two-dimensional Structure

M

V T′

𝜽↓e↑∗ 

•  An analytic but highly idealized nonlinear axisymmetric tropical cyclone model has been formulated.

•  TC can be maintained in an intense steady state without any contribution from ambient conditional instability.

•  The absence of TC when SST<26℃ is due to the shallow depth of the conditional neutral or unstable layer.

•  The model of TC can be imagined as a simple Carnot heat engine.

•  The boundary later physics and the dynamics of the eye have not been accounted for properly.

Conclusions