Wind loading and structural response
Lecture 1 Dr. J.D. Holmes
Meteorology of Windstorms
Meteorology of windstorms
• Types of storms producing extreme winds :
• extra-tropical depressions (gales)
• synoptic scale
40-60° latitude
• tropical cyclones (hurricanes, typhoons)
• synoptic scale
5°-30° latitude oceans and coast
• thunderstorms (downbursts, tornados)
• meso scale
0°-50° latitude
local convection
• downslope winds (chinook, Santa Ana)
• meso scale certain topographic situations thermally driven
Meteorology of windstorms
• Forces acting on air in horizontal motion :
• Pressure gradient - pressure differences created by non uniform solar heating
• Coriolis force - (apparent) force due to the earth’s rotation
• Centrifugal force - air moving with small radius of
curvature
• Frictional forces - due to earth’s surface -significant at
lower heights (boundary layer)
Meteorology of windstorms
• Pressure gradient force :
z
p y z
x
y
(p+
p
x) y z
x
p x y z
Net force = 
x
p
Net force per unit volume = x
Pressure gradient force per unit mass =
 1  p
  
 ρa  x
Meteorology of windstorms
• Coriolis force :
• an apparent force due to the rotation of the earth
(S. Pole)
AA =  U (t)2 = (½)a (t)2
a=2U
Meteorology of windstorms
• Coriolis force :
• acts to the right of the direction of motion in the northern
hemisphere, and to the left of the velocity vector, in the
southern hemisphere
• Coriolis force per unit mass (acceleration) = 2U  sin 
= fU
 = angle of latitude  = angular velocity of the earth
f= 2 sin 
Coriolis force is zero where  and f are zero
i.e. at Equator
Meteorology of windstorms
• Geostrophic wind :
• Balance between pressure gradient and Coriolis forces
• Approximates wind speed in upper atmosphere
• Ugeostrophic
 1

= 
 ρa f
 p

 x
Meteorology of windstorms
• Geostrophic wind :
• Flow parallel to isobars
• Anti-clockwise rotation around low pressure centre in N. Hemisphere
Meteorology of windstorms
• Cyclonic systems :
• Anti-clockwise rotation in Northern Hemisphere
Clockwise rotation in Southern Hemisphere
•
direction of Coriolis force determines direction of rotation
in cyclones including hurricanes
Near the equator ( < 5° N), hurricanes cannot form
Meteorology of windstorms
• Gradient wind :
Includes centrifugal force : (U2/r) per unit mass
r = radius of curvature of isobars
• Equation of motion :
anti-cyclone
cyclone
U2
1 p
 fU
0
r
 a r
U2
1 p
 fU
0
r
 a r
Quadratic equations for gradient wind speed, U
Meteorology of windstorms
• Gradient wind :
• Solutions :
anti-cyclone
U
cyclone
U 
fr
2

fr
2

f 2 r 2 r p

4
 a r
f 2 r 2 r p

4
 a r
U is limited to f r for an anti-cyclone, but unlimited for a cyclone
2
Meteorology of windstorms
• Frictional effects in ‘boundary layer’ :
• Friction at earth’s surface acts in opposite direction to flow
new force balance - component towards low pressure region as height decreases
Direction change with height - Ekman spiral <30o
Meteorology of windstorms
• Characteristics of hurricanes :
• Known as ‘typhoons’ in S. China sea and elsewhere as ‘tropical cyclones’
•
Can exist between 5 and 40 latitude
full strength between 10 and 30 latitudes
• Require ocean temperature greater than 26 Celsius (79°F)
taken to higher latitudes by warm ocean currents
• 3-dimensional vortex structure with ‘eye’ of calm winds
Meteorology of windstorms
• Characteristics of hurricanes :
(S. Hemisphere)
• 3-dimensional vortex structure with ‘eye’ of calm winds
Meteorology of windstorms
• Variation of wind speed/direction at a point in a hurricane :
Wind
speed
Direction
(Figure 1.7 in book shows low wind speed in ‘eye’)
Meteorology of windstorms
• Wind field of hurricanes :
Meteorology of windstorms
• Wind field of hurricanes :
Meteorology of windstorms
• Saffir-Simpson scale for hurricanes :
Category
Central Pressure
millibars
I
II
III
IV
V
> 980
965-979
945-964
920-944
< 920
inches of
Hg
> 28.9
28.5-28.9
27.9-28.5
27.2-27.9
< 27.2
Windspeed (mph)
1-min.
3-sec
Surge
(ft)
74-95
96-110
111-130
131-155
> 155
94-121
122-140
141-165
166-197
>198
4-5
6-8
9-12
13-18
> 18
Damage
Potential
Minimal
Moderate
Extensive
Extreme
Catastrophic
Meteorology of windstorms
• Profiles of pressure and gradient windspeed :
pressure
p  po
  A
 exp  B 
pn  po
r 
Holland (1980)
pressure gradient
p
AB
  A
 p B 1 exp  B 
r
r
r 
p = pn-p0 where p0 is central pressure
gradient wind speed
f 2 r 2 Δp AB
A
U


exp(

)
2
4
ρa r B
rB
fr
Meteorology of windstorms
pressure
profile
Pressure at
sea level (mb)
• Profiles of pressure and gradient wind :
1010
1000
990
980
970
960
950
940
0
10
20
30
40
50
gradient wind
speed profile
Gradient wind speed
(m/s)
Radial distance from centre (km)
60
50
40
30
20
10
0
0
10
20
30
40
Radial distance from centre (km)
50
Cyclone ‘Tracy’
1974
Meteorology of windstorms
• Thunderstorm winds :
• Severe winds in small areas generated by strong downdrafts and
tornadoes
• Conditions for generation of downdrafts
– High wind shear
– Supply of warm moist air at ground level
– Uplift mechanism
• Melting hail cools surrounding air
– initiates downdraft
– augmented by evaporating rain
• Extreme winds are dominated by thunderstorm downdrafts in many
locations : Argentina, South Africa, Central U.S., Singapore ….
Meteorology of windstorms
• Downbursts :
• Macrobursts : > 4 km in horizontal extent
• Microbursts : < 4 km in horizontal extent
cumulus
cloud
warm air
cool air
•
Largest documented wind speed : 67 m/s (130 knots), Andrews Air Force
Base, Maryland, 1983
(anemometer record : Fig. 1.9 in book)
Meteorology of windstorms
• Downburst anemometer record :
Max gust
1 hour
Wind
speed
Direction
Meteorology of windstorms
• Downburst wind speed footprint :
15m/s
20
Direction of storm
30
40
50
Meteorology of windstorms
• Tornadoes :
Funnel-shaped vortex created in thunderstorms
Meteorology of windstorms
• Tornadoes :
‘Supercell’ - intense convective cell
Meteorology of windstorms
• Tornadoes :
• Narrow width - typically 100 metres can be up to 1000 m
• Can travel long distances before dissipation - up to 50 km (30 miles)
• Most common in mid-West of U.S. (esp. Oklahoma, Kansas)
also occur in Argentina, South Africa, India, Russia, Australia
Meteorology of windstorms
• Tornadoes - Fujita scale:
F-Scale (Wind
Speed Range)
F0 (40-72 mph)
Number of
Tornadoes Percentage
Observed in
U.S. 1950-94
11,046
31.3
Cumulative
Percentage
31.3
F1 (73-112 mph)
12,947
36.7
68.0
F2 (113-157 mph)
7,717
21.9
89.9
F3 (158-206 mph)
2,523
7.2
97.1
F4 (207-260 mph)
898
2.6
99.7
F5 (261-318 mph)
121
0.3
100.0
35,252
100.0
TOTAL
Meteorology of windstorms
• Regions exposed to tornadoes (ASCE 7-95):
Meteorology of windstorms
• Tornado wind field:
• Can be modelled as a Rankine (combined) vortex:
Tangential
velocity
Radial Vr  0.5V
Vertical Vv  0.62V
Static
pressure
Meteorology of windstorms
• Tornado damage footprint :
Meteorology of windstorms
• Downslope winds :
• Thermally driven - several different phenomena
• usually occur on the lee slopes of mountains, or in valleys
• U.S. : chinook winds (Colorado)
Santa Ana winds (California)
• Affect small areas
• Dealt with in wind loading codes as ‘special wind regions’
End of Lecture 1
John Holmes
225-405-3789 JHolmes@lsu.edu