L20 Tornadoes: cyclostrophic balance

L20 Tornadoes: cyclostrophic balance

Ahrens Chapter 7/8: Precipitation

Section on Hail

Chapter 14/15: Lightning & Thunder

Supercell thunderstorms

• Rotating updraught– Rotation causes the storm to be more robust

– longer-lived, and therefore more dangerous

• Forms an area of low pressure at centre of rotation, called a mesolow

• Updraught centred on the low pressure

• Circulation around the low is in cyclostrophic balance…

Cyclostrophic balance

Acceleration (= Force/mass)given by: v2/r

v ~30 m s-1

r ~1000 m

v2/r ~0.9 m s-2

•Rotating air in a supercell generates an area of low pressure at the centre of the rotating updraught.

•The circulation is in ‘cyclostrophic balance’, where the pressure gradient force (PGF) is balanced by a ‘centrifugal force’ (really a centripetal acceleration) Centrifugal

Force =

PGF

Lv

r

mv2

r

Tornado/supercellcase

Doesn’t this look a bit familiar?

CoriolisForce

PGF

Lv ~ 10 m s-1

Geostrophic Balance

r ~ 500 km

Centripetal accelerationgiven by: v2/r

v ~10 m s-1

r ~500000 m

v2/r ~0.0002 m s-2

Centripetal acceleration much smaller than the supercell case.

Coriolis force is due to planetary rotation

Centrifugal force (or centripetal acceleration) is due to ‘local’ rotation

Large-scaleweathersystem

Coriolis Force

sin2f

Apparent force that acts on anythingthat moves in the Earth’s rotating frameof reference.

Coriolis parameter, f:

f is zero at equator, maximum at poles

mfvCF v = 10 m s-1

CF/m =0.0011 m s-2

At 50°Nf = 1.1 x 10-4 s-1

is the Earth’s rotation rate = 2 radians per day, or, in SI units (seconds): = 2 /(24x60x60) per second = 7.27 x 10-5 s-1

Comparing Coriolis & centrifugal forces

CoriolisForce

PGF

Lv ~ 10 m s-1

Geostrophic Balance

r ~ 500 km

Centripetal accelerationgiven by: v2/r

v ~10 m s-1

r ~500000 m

v2/r ~0.0002 m s-2

Coriolis force is due to planetary rotation

Centrifugal force is due to ‘local’ rotation

Coriolis accelerationgiven by: fv

~0.0011 m s-2

Is bigger, but in some casesthe centripetal acceleration isimportant at synoptic scales;But Ignore for now!

CentrifugalForce =

PGF

Cyclostrophic balance

Lv

r

mv2

Centripetal accelerationgiven by: v2/r

v ~30 m s-1

r ~1000 m

v2/r ~0.9 m s-2

•Rotating air in a supercell generates an area of low pressure at the centre of the rotating updraught.

•The circulation is in ‘cyclostrophic balance’, where the pressure gradient force (PGF) is balanced by a centrifugal force

Coriolis accelerationgiven by: fv

~0.0033 m s-2

Is much smaller thancentripetal: can ignoreCoriolis force for small scalerotations: storms/tornadoes

Summary of forces for rotating systems

• Supercell storms/tornadoes (~1 km across):– Cyclostrophic balance:– PGF vs. centrifugal force (ignore Coriolis)

• Synoptic weather systems (~1000 km):– Geostrophic balance:– PGF vs Coriolis Force (ignore centrifugal)

• Scale is all-important!

Back to Supercell storms

• Low pressure in rotating updraught can be so low that is causes saturation and forms a ‘funnel’ cloud

• (Drop in pressure is equivalent to ascent)

Tornadoes from supercell storms

Funnel cloud

Dust/debrisstirred upat surface

Pylonfor scale

Supercells & Tornadoes in the UK

• Generally much less severe than a typical US supercell/tornado, nevertheless…

• The UK experiences around 40 tornadoes a year – they generally do not cause damage, or are not even noticed

• A couple of recent cases:– 21st March 2004 – S. Midlands– 28th July 2005 – Lincolnshire– Data & images from www.torro.org.uk

UK Tornadoes by Month Percentages 1960 - 1999 (Reynolds)

From Royal Met Soc talk by Nigel Bolton, 2010

Damage in Oxfordshire

Also accompanied by 2cm diameter hail

UK supercell storm: 28th July 2005

Nottingham Skew T-log P – large CAPE

Path of two supercells:Right-moving is the strongest

Nr Peterborough, 28 July 2005

Damage nr. Peterborough

Images of the Day, 28/07/05

Farnborough, Dec. 2006

Spatial scale of storms

• Tornadoes are generally very localised, but can cause severe damage on small scales (100’s metres)

• Met: Weather and Climate (next semester), covers larger scale storms: tropical cyclones (hurricanes), also mid-latitude cyclones in more detail.

Hurricane Katrina, August 2005

Summary: Tornadoes

• Small scales (~1 km across)• Flow close to cyclostrophic balance:

– PGF in balance with a centrifugal force– strictly: PGF creates a centripetal acceleration– Ignore Coriolis force at these small scales– cf. Geostrophic balance in synoptic weather systems

• Tornadoes are an important hazard in the UK (as well as other parts of the world): they can cause very localised severe damage

Hail formation

• Starts with small ice crystal surrounded by abundant supercooled droplets – within a cloud with strong updraughts

• Growth by riming• Once initial crystal

shape is lost: graupel

Typical hail pellets~0.5 cm

Grapefruit-sized hailstones~10 cm

Serious Hazard

Hailstone structure

• Hail can grow quite rapidly (5-10 minutes)• As it grows, requires larger and larger updraught

velocities to support it• One path is approximately horizontally across

the cloud, growing as it traverses the updraught, then plummeting as it enters the downdraught

• Alternating light/dark layers due to different growth stages – dark layers have bubbles trapped; ‘wet’ growth vs ice (colder) growth

Cloud electrification

• Need a cold cloud – i.e. contains ice• Radar data indicates graupel or hailstones• As hail falls through cloud, bumping into

other cloud particles, it tends to become negatively charged

• Exact mechanism is not clear, but falling hail tends to make the lower cloud negatively charged, and leaves the upper part of the cloud positively charged…

Lowest part of cloudoften weakly positivelycharged

Lightning discharge

• Air has a low conductivity, but it can only cope with a gradient in charge (an electric field) up to ~106 volts per metre – beyond that it discharges: Lightning.

• 3 types of lightning:– 1a Within cloud– 1b Cloud to air– 2 Cloud to ground – most

energetic

Produce cloud flashes}

Lightning time sequence:1. Stepped Leader

Initial chargedistribution

Preliminarybreakdown inlower cloud – neutralizes the positive charge in cloud base

‘Stepped Leader’ advances in ~50 m steps, in 1 stime period between steps ~50 s

Downwards spread of negative charge induces a positive charge at ground

2. Attachment and 1st Stroke

Stepped leadercontinues advance

When within ~10-100 m of the highest objects, a discharge moves up from the ground to meet the downwards advancing stepped leader

Once connected, large flow of electrons to ground – the ‘return stroke’- Intense flash

3. Dart leader, subsequent strokes

New regions of negative charge in the cloud are connected

Dart leader moves down the mainpath followed by the first stroke, sending more electrons downwards

Further stroke;

Usually 3 or 4 strokes to discharge the cloud.Charge can build up again in as little as 10s

NB Time-lapse photograph – many processes superimposed!

Can see a range of stepped leaders, together with the path of the main stroke (re-used for subsequent strokes)

Thunder• Return stroke raises air temperature in the channel it passes

through to >30,000K very quickly – air has no time to expand, so pressure rises, and air expands rapidly.

• Creates a shock-wave, which then creates a sound-wave a little further away: thunder

• Travels at speed of sound: 330 m s-1 (i.e. 1 mile in ~5 seconds)

• Stepped leaders also create thunder, but much less than the main stroke

• Sound waves tend to be refracted upwards, limiting the range over which thunder can be heard to within ~25 km of the source.

Days with thunder (1971-2000)

Distribution of lightning

Global Electrical Circuit

Thunderstormsare the ‘batteries’driving the circuit

Blue Jets, Red Sprites, etc.

These are allfairly recentlydiscovered electricalphenomena, closelyassociated withthunderstorms, that probably play a rolein the global electricalcircuit.

Summary

• Hail– Produced in cold clouds, multiple ascent and descent

cycles with growth by riming

• Lightning– Falling hail is negatively charged, leaving upper cloud

positive, lower cloud negative– Stepped leader; Return stroke; Dart leader;

subsequent strokes– Global electrical circuit driven by thunderstorms

• Thunder– Sound wave from 30000K heating by lightning stroke