Tropical Cyclones

Heat & Momentum Structures

Tropical CyclonesPrimary circulation: tangential (rotational) wind; cyclonic

Strongest at low levels (lowest 2 km of troposphere), extends throughout depth of troposphere; strongest in eyewall

modelobservations

Thermal and Tangential Wind RelationshipTangential winds decay with height due to the warm center of

the vortex, as opposed to an extratropical cyclone.Below equation is in Cartesian form. If one flips the

temperature gradient vector with respect to radius (analogous to latitude here) and defines ug as tangential wind speed, one can see an increase with tangential wind with height for a cold

core vortex, while the opposite will occur for a warm core vortex.

Tropical Cyclones

observations

model

Tangential winds typically strongest just above PBL, though vertical profile is dependent upon quadrant and other storm characteristics, such as shear and convection

Tropical CyclonesSecondary

(Transverse)

circulation: In, Up &

OutVital in intensity change

LL inflow, UVM in

eyewall, UL outflow

Dual Doppler and MM5 radial wind speed

Dual Doppler vertical wind speed

dropsonde radial wind speed

Most inflow is focused in the PBL

Tangential wind speeds

decrease with height

Radial winds become more outward with height, inflow

in right quadrants,

and reversed flow in eye

storm relative radial wind speedground relative tangential wind speed

Strong surface low pressure weakens with height, and reverses sign in eyewall (LH release)

D-values

Tropical Cyclones

Response to heat and momentum sources:Strongly stratified air in the vertical (high

static stability) is resistant to vertical motion. Air moves radially.

Areas of high inertial stability are resistant to horizontal motion. Air moves vertically.

Heat and Momentum SourcesNeed to figure our how responds to heat and

momentum sources- important to air flow.Go to Kuo-Eliassen equation…

A(δ2ψ/δy2)+ 2B(δ2ψ/δyδp) + C(δ2ψ/δp2) + D(δψ/δy) + γ(δH/δy) + (δχ/δp)

Sources of heat, H:H = -(δ/δy[θ*v*]+δ/δp[θ*w*]) + [θ]/[T]

Sources of momentum, χ: χ = δ/δy[u*v*]+δ/δp[u*ω*] + [Fx]

Heat and Momentum Sources

We will now examine air flow in response to heat and momentum sources via diagrams…

-ln P

y

+

Heat SourceδH/δy > 0 δH/δy < 0

+

-

-ln P

y

Heat Source

v =δψ/δP

+

+

-

ω = - δψ/δy ~ -w

ψ is proportional to δH/δy

-ln P

y

Momentum Source

δχ/δP > 0

+

+

-δχ/δP < 0

-ln P

y

Momentum Source v =δψ/δP

ω = - δψ/δy ~ -w

+

-

ψ is proportional to δχ/δP

Heat and Momentum FieldsResponse is crucial in hurricane vortex.

Eyewall: heat source.Loss of angular momentum to sea surface:

momentum sink.

Low-level flow goes from high values of absolute angular momentum in outer synoptic environment

to the eyewall.

Heat and Momentum FieldsDefine AAM:

AAM = r(V + ½ fr)Large r in synoptic environment leads to high AAM

values. Very low AAM in eye (small r, small tangential velocity). Air flows from high AAM to low

AAM.Gradient of AAM tied to inertial stability, IS.

Heat and Momentum FieldsLow level flow well away from the eyewall is in an

environment of low inertial stability and, thus, moves horizontally.

As low level flow from the outer environment approaches the eyewall, winds increase dramatically. Just inside of

radius of maximum winds (RMW), inertial stability is often maximized.

So, air turns upward in the eyewall but hits the high static stability of the tropopause. Then, it will transition from moving upward to outwards, where inertial stability is

weaker. General UL outflow results.

Heat and Momentum Fields

Heat and Momentum Fields

Temperature Anomalies:warm core, especially at

mid and upper levels

CISK and WISHECISK = Conditional Instability of the Second Kind

-Need a disturbance-Braking mechanisms include low-mid level dry air,

high VWS, low SST/OHC-If latent heat release has less energy than frictional deceleration causing the convergence, that will also

cause weakening

CISKFrictional inflow and Ekman pumping help to lift air to LCL

As the air rises thereafter, it releases LHTemperature increases, air column expands

SLP drops, especially if deep convection near centerPressure gradient increases

Tangential wind speed increases and inflow increasesIncreased inflow increases frictional convergence

Increased moisture convergence and LH release, etc…see a tendency for a positive feedback loop

CISK and WISHEWISHE = Wind Induced Surface Heat Exchange

Air moves isothermally, crossing angular momentum surfaces as it heads inwards in PBL

and outwards at ULMoves along constant AAM surface in the

eyewall, moving upwards and moist adiabaticallyIsothermal in PBL, even though P and q – heat

added from conduction and frictional deceleration of wind due to sea surface

WISHE

Temperature gradient between SST and tropopause is potential energy

Potential Intensity (PI) of storm can be calculated knowing those temperatures

Moist convection can help convert potential energy into kinetic energy by altering pressure

fields, which then affect wind

Energy associated with LH and SH fluxes

Sensible heat flux: SH = ρacp|v|cd(Ts-Ta)

Latent heat flux: LH = ρaL|v|cd(qs-qa)where ρa = air density (~1.2 kgm-3)

Cp= specific heat at constant pressure (1006 Jkg-1K-1)

|v|= wind speed in ms-1

cd= drag coefficient

Ts= SST

Ta = 10 m air temp

L = latent heat of evaporation or “vaporization” (2.5x106 Jkg-1)qs= mixing ratio of air at sea surface

qa = mixing ratio of air at 10 m

Energy associated with LH and SH fluxes

Limitations: fluxes only show the ocean-atmosphere interface and neglect the atmosphere’s vertical

structure.In the winter, you can get large fluxes, but the atmosphere is not as conducive for TCs due to limited moisture availability (as well as often

increased vertical wind shear, which would reduce the effectiveness of heating).

Heat & Momentum Fields

*High inertial stability focuses eyewall convection

*LH release leads to SLP drops

*SLP drops at center increase the pressure

gradient*Greater pressure gradient

intensifies primary and secondary circulations

Potential Vorticity in TCs

Potential vorticity generally consists of planetary, relative, and stretching vorticity.

Very high absolute vorticities due to large relative vorticity values

Relative and Potential VorticityAlong the inner portion of the eyewall, an annulus of high PV exists, largely due to relative vorticity (moisture can also

help). Vorticity gradients exist on either side of the eyewall,

which can trigger barotropic instability- especially on

inside- for disturbances to use for energy for wave growth.

Vorticity EvolutionVortex Rossby waves and mesovortices can form from the

instability and mix eye & eyewall air. This reduces maximum tangential velocity in the eyewall but spins up the eye.

END

Next powerpoint includes intensification and weakening of TCs, as well as formation of eye

and evolution of hurricane inner core.