Topic 2
Tropical Storms, Wind Structure and
Mean Velocity in the ABL
Dr. Jin Wang
Sep 18, 2023
1
Contents
1. Boundary Layer Winds
2. Wind Structure
3. Mean Velocity Profiles
4. Wind Spectrum & Scales
5. Non-synoptic winds: downbursts & tornadoes
2
Boundary Layer Winds
3
Atmospheric Boundary Layer Flow
As the earth’s surface is approached, the frictional forces play an
important role in the balance of forces of moving air. The region of
frictional influence is called the ‘atmospheric boundary layer’.
4
Atmospheric Boundary Layer Flow
Balance of forces in the ABL
Wind velocity spiral in the ABL
5
Wind Structure
6
Wind Velocity Components
• Velocity in x-direction
U(t) = U + u(t) or U + u’
where U is the mean and u’ is the fluctuating component.
• Velocities in y and z-direction
V(t) = v(t) or v’
W(t) = w(t) or w’
7
Wind Velocity Components
• In more rigorous terms, let x, y, z be a
Cartesian reference system with origin in
O on the ground; z is vertical and
directed upwards. The wind field is
represented by the vectorial temporal
law of velocity at point M of coordinates
x, y, z:
U(M) = i u(z)
U (M; t) = i u (M; t) + jv (M; t) + kw‘ (M; t)
• The wind field is represented by the
vectorial temporal law of velocity at
point M of coordinates x, y, z:
U(M; t) = U(M) + U (M; t)
8
The Wind Structure
 Not steady, but fluctuating and gusty

does not vary significantly over a 10 min.
interval period to 1 hour; local stationarity

decreases near the ground; mean
velocity profile

(fluctuating component); more or less
constant at all heights
 Longer duration disturbances = correlated
 Short duration gusts = non correlated
U  p (pressure on structures)
Fig. : Record of Wind Speed at Three Heights on
a 150 m (500 ft) Mast in Open Terrain (Sale East,
Victoria, Australia – E.L. Deacon)
Local stationarity (10 min. – 1 hour) BUT: 4
day variations
9
Wind Turbulence
• Wind speed can be considered as two components; mean wind speed
and fluctuating component (U+u’)
• Fluctuating component (turbulence) caused by convective movement
(meteorological) and/or by ground roughness (mechanical turbulence)
• In boundary layer at high wind speed, it is assumed that mechanical
turbulence predominates; this is of interest to engineers
• Turbulence (mechanical) is higher in rougher terrain than in smoother
terrain; e.g. suburban vs. flat open terrain.
• Turbulence (mechanical) decreases with increasing height above
ground.
• Turbulence (gust) parameters of importance are:
• turbulence intensity (standard deviation of fluctuations
normalized by mean wind speed)
• gust/eddy frequency
• gust/eddy size (wind snapshot) referred as integral scale
10
Wind Turbulence
• Tendency of mean wind speed to stay relatively steady over periods
of 10 min to an hour is significant stationarity basic idea to wind
tunnel testing.
• Explanation of steadiness lies in the fact that processes generating
the mean flow have time scales >> 1 hour.
• However, mean speed does vary with time; large fluctuations cover
a period of several days
11
Mean velocity profiles
12
Atmospheric Boundary Layer Flow
As the earth’s surface is approached, the frictional forces play an
important role in the balance of forces of moving air. The region of
frictional influence is called the ‘atmospheric boundary layer’.
13
Variation of Wind Speed with Height
• Ground obstructions retard the movement of air close to the
ground surface, causing a reduction in wind speed.
• At some height above ground, the movement of air is no longer
affected by ground obstruction. This height is called gradient
height, Zg, which is a function of ground roughness.
• The unobstructed wind speed is called gradient wind speed, Ug. It
is constant above gradient height.
• The power law is generally used by engineers to represent variation
of wind speed with height. It is an empirical equation.
• The logarithmic law is used by meteorologists/engineers. It is based
on physics of the boundary layer. It is valid in the bottom 20 to 30%
of the boundary layer
14
Logarithmic Law
• The logarithmic law was originally derived for the turbulent
boundary layer on a flat plate by Prandtl; however, it has been
found to be valid in an unmodified form in strong wind
conditions in the atmospheric boundary layer near the surface.
• The wind shear, i.e., the rate of change of mean wind speed
with height is a function of the following variables:
 the height above the ground
 the retarding force per unit area exerted by the ground
surface on the flow – known as the surface shear stress,
 the density of air,
• Near the ground, the effect of the earth’s rotation (Coriolis
forces) is neglected.
15
Logarithmic Law
∗
where:
z0 = roughness length
u* = friction velocity
o = shear stress at the ground surface
ρ = air density
k = Karman’s constant ~ 0.4
16
Example
∗
∗
∗
Example 1.xlsx
17
The Deaves and Harris mean wind profile
• The logarithmic law is applicable to strong winds with thermally
neutral stability for heights in the surface layer up to 100-200 m,
a height range which includes most structures.
• The Deaves and Harris (D& H) model attempts to provide a
consistent mathematical model for the complete atmospheric
boundary layer up to the gradient height,
∗
∗
18
Power Law
19
Aerodynamic Roughness over Different Types
of Terrains
Z0 and  are
functions of ground
roughness. Typical
values of Z0 and  are
given in the following
table.
Values of gradient height, ZG, power law exponents , and the roughness len
Terrain Terrain description
Gradient Roughness
Mean
category
height,
length,
speed
z𝑍G
zo
exponent
(m)
(m)

1
2
3
4
Open sea, ice, tundra,
desert
Open country with low
scrub or scattered trees
Suburban areas, small
towns, well wooded areas
Numerous tall buildings,
city centres, well
developed industrial
areas
250
0.001
0.11
300
0.03
0.15
400
0.3
0.25
500
3
0.36
20
Matching of the Two Laws
α is also related with Z0 as follows
⁄
Where
is a reference height at
which the two ‘laws’ are matched.
Figure Comparison of the logarithmic (
and power laws (
) for mean velocity
profile.
21
Power Law Exponent
22
Homogeneous Terrain
23
Example
Consider a change of terrain roughness from 1=1/7 to 2 =1/3 and a
corresponding change of gradient height from zg1 =274 m to zg2 =457 m.
Suppose V1=50 m/s at z1=20 m. What is the wind speed at 20 m above the
location 2. (i.e. at z2=20 m)?
Soln:
 z1 

U1 = U g 
z 
 g1 
1
2
 z2
U2 = Ug 
z
 g2




 z2
U 2 = U1 
z
 g2




Dividing 2 by 1 and rearranging
2
 z g1 


 z1 
1
Therefore, the wind speed at 20m above ground at location 2 is
1/ 3
1/ 7
 20   274 
U 2 = 50
 

 457   20 
= 25.6m / s
24
Transition Terrain
25
Transition Terrain
Developing wind profile (ESDU 82026)
26
Transition Terrain
Smooth to rough transition
27
Example
28
Transition Terrain
Illustration of wind profiles at the site, and upwind
and far downwind of the change in roughness (ESDU
74026)
29
Wind spectrum & scales
30
Wind Spectrum and Scales
•Describes better these wind fluctuations
•Power spectrum = a representation of the fluctuating energy with
frequency: FFT (time series)
•For a very long record (several years); various speed and direction
fluctuations
Synoptic wind spectrum & scales; description of the distribution of wind
energy with frequency
Variation of Mean Velocity in the
Atmospheric Boundary Layer
31
Wind Spectrum (Van der Hoven 1957)
Idealization of the Wind Speed Spectrum
Over an Extended Frequency Range
32
Comments for the Wind Spectra
• Two “humps” and a “gap”
• Energy appears into two major humps (T = 4 days movement of
large-scale pressure systems (T = 1-day diurnal frequency), T = 1
min associated with turbulence) separated by a gap (T = 10 mm to
1 hour)
• Turbulence is created through surface drag
• The higher the mean velocity, the larger the turbulence production
and the higher spectrum in storm winds
• The gap enables a convenient distinction between “mean wind”
and “gusts”
• Choice of an averaging period for mean wind of 1 hr to 10 mm
provides fairly stable mean values (thunderstorms may be an
exception).
• Therefore, it is possible to assume that synoptic wind turbulence is
a stationary Gaussian random process.
33
Structure of Wind Turbulence
• Tendency of mean wind speed to
stay relatively steady over periods
of 10 min to an hour is significant
stationarity basic idea to wind
tunnel testing.
• Explanation of steadiness lies in
the fact that processes
generating the mean flow have
time scales >> 1 hour.
• However, mean speed does vary
with time; large fluctuations
cover a period of several days
34
Statistical Description of Random
Wind Fluctuations
• In more rigorous terms, let x, y, z be a Cartesian reference system with origin in
O on the ground; z is vertical and directed upwards. The wind field is
represented by the vectorial temporal law of velocity at point M of coordinates
x,y,z:
• The wind field is represented by the vectorial temporal law of
velocity at point M of coordinates x, y,z:
Longitudinal velocity: U(M; t ) = U(M; t ) + u(M; t )
35
Turbulence Intensity
 The general level of turbulence or ‘gustiness’ in the wind speed
in storm winds, can be measured by its standard deviation or
root-mean-square.
→
 The ratio of the standard deviation of each fluctuating
component to the mean value is known as the turbulence
intensity of that component:
Longitudinal:
Lateral:
Vertical:
36
Wind Spectra
In order to describe the distribution of turbulence with frequency,
a function called the spectral density, often abbreviated to
‘spectrum’, is used. It is defined so that the contribution to the
variance ( , or square of the standard deviation), in the range of
frequencies from to
, is given by
, where
is
the spectral density function for velocity component
.
There are many mathematical forms that have been used for
in meteorology and wind engineering. One of the most
common models for the longitudinal velocity component is the von
Karman form (developed for laboratory turbulence by von Karman,
1948, and adapted for wind engineering by Harris, 1968).
37
von Karman Spectra
There are many mathematical forms that have been used for
in meteorology and wind engineering. One of the most
common models for the longitudinal velocity component is the von
Karman form (developed for laboratory turbulence by von Karman,
1948, and adapted for wind engineering by Harris, 1968).
Longitudinal spectra:
/
𝑛 𝑆 (𝑛)
𝜎
𝑛𝐿
𝑈
38
Turbulence Integral Length Scale
 The velocity fluctuations in a flow passing a point may be
considered to be caused by a superposition of conceptual eddies
transported by the mean wind. Each eddy is viewed as causing that
point a periodic fluctuation with frequency . By analogy with the
case of the traveling wave, we define the eddy wave length as
. The wave length is a measure of eddy size.
 Integral scales of turbulence are measured of the average size of
the turbulent eddies of the flow. There are altogether nine integral
scales of turbulence, corresponding to the three dimensions of the
eddies associated with the longitudinal, lateral, and vertical
components of the fluctuating velocity.
is the auto-covariance function of the fluctuation u.
39
Example
Calculate the integral scale and spectra of longitudinal
velocity
Example.m
40
Gust Factor
• In many design codes and standards for wind loading, a
peak gust wind speed is used for design purposes. The
nature of wind as a random process means that the
peak gust within a sample time, T, of, say 10 minutes is
itself also a random variable.
• The gust factor, G, is the ratio of the expected
maximum gust speed within a specified period to the
mean wind speed.
41
 gust factor
uˆ = u + g u u
instantaneous peak speed
3-sec averaged peak speed
Gu ( ) =
uˆ ( ) = u + g u ( ) u ( )
gust factor
Gu =
uˆ

= 1 + gu u = 1 + gu Iu
u
u
Gu ( ) =
 ( )
uˆ ( )
= 1 + g u ( ) u
u
u
uˆ ( )
 ( )
 ( )
= 1 + g u ( ) u
= 1 + g u ( ) I u u
= 1 + g u ( ) I u P0
u
u
u


 u =  Su ( f )df
2
gust factor
 ( ) =  S u ( f ) ( f , )df
2
u
0
0
g u ( ) = 1.175 + 2 lnTVe 
1/ 2

P0 ( ) = 
0
Su ( f )
u2
( f , )df
sin 2 (f )
( f , ) =
(f )2
 gust factor Gu ( ) ： method 1 (frequency domain)
g u ( ) = 1.175 + 2 lnTVe 
1/ 2
fS u ( f )
 u2
=
4 fu
(1 + 70.8 f )
u
5
2 6
 = 3 sec T = 3600 sec I u = 0.1968
fL
fu = u
u

 u ( ) =  Su ( f ) ( f , )df = 5.2633
2
2
sin 2 (f )
( f , ) =
(f )2

 ( ) =  (2f ) 2 Su ( f ) ( f , )df = 2.854 2
2

u
0
0
1  u ( )
Ve =
= 0.0863
2  u ( )


P0 ( ) = 
0
g u ( ) = 1.175 + 2 lnTVe 
1/ 2
Gu ( ) =
u = 35m / s Lu = 69.804m
Su ( f )
u2
( f , )df = 0.5839
= 3.557
uˆ ( )
 ( )
 ( )
= 1 + g u ( ) u
= 1 + g u ( ) I u u
= 1 + g u ( ) I u P0 = 1.53
u
u
u
 gust factor Gu ( ) ： method 2 (time domain)
1/ 2

 ~ P  
g u ( ) = 1.175 + 2 ln T 1  
P0  


~ =
U z
P0 =
1
= 0.569
1 + 0.56~ 0.74
Luz
= 1.504
 = 3 sec T = 3600 sec I u = 0.1968
u = 35m / s Lu = 69.804m
~ TU z
T =
= 1805
Luz
P1
1
=
= 0.0178
P0 31.25~1.44
1/ 2

 ~ P  
g u ( ) = 1.175 + 2 ln T 1  
P0  


Gu ( ) =
= 3.485
uˆ ( )
 ( )
 ( )
= 1 + g u ( ) u
= 1 + g u ( ) I u u
= 1 + g u ( ) I u P0 = 1.52
u
u
u
Tropical storms, hurricanes &
typhoons
45
Large Scale Storms
• Hurricanes (also called Tropical Cyclones, Typhoons):
• Generally, originate between 5° and 30° latitudes.
• Sustained surface wind speeds of 74 mph or more.
• Require ocean temperature greater than 26° Celsius (79°F) taken to
higher latitudes by warm ocean currents.
• Tropical cyclones are translating vortices with diameters of hundreds of
miles and counterclockwise (clockwise) rotation in the northern
(southern) hemisphere.
• Their translation speeds vary from about 3 to 30 mph.
• Hurricanes are classified in accordance with the Saffir-Simpson scale
46
Saffir-Simpson Hurricane Scale
https://www.nhc.noaa.gov/video/SSHWS_animaton.mp4
47
Hurricane prone regions
Source: Williams and Leatherman. 2008. Hurricanes: Causes, Effects, and the Future
48
Satellite image of a hurricane
Source: Williams and Leatherman. 2008. Hurricanes: Causes, Effects, and the Future
49
Formation of hurricanes
Source: Williams and Leatherman. 2008. Hurricanes: Causes, Effects, and the Future
50
Hurricane flow structure
• Gradient level wind speed (Vgr) estimation;
useful for hurricanes, typhoons because of:
• destruction of surface instruments
• infrequency of these storms
𝑉
Track
𝑉
• Particularities
• strong curvature of isobars
• weak Coriolis effect (near equator)
• strong translation
with translation
𝑉
𝑉
𝑉
𝛼
𝑟
without translation
Tropical storm
51
Hurricane flow structure
or
Fig. Rankine Vortex
based on Rankine vortex
52
Hurricane velocity record
Source: Williams and Leatherman. 2008. Hurricanes: Causes, Effects, and the Future
53
The velocity profile is treated like synoptic wind
54
Non-synoptic winds: downbursts &
tornadoes
55
Local storms: tornados
• Thunderstorms can also produce one
of the most destructive types of wind,
i.e. the tornado. Maximum wind
speeds in a tornado can reach over
100 m/s (224 mph).
• Rather like in a Hurricane, but on a
much smaller scale, air moves
towards the low pressure in a spiraling
manner before turning upwards near
the eye of the tornado.
• Tornadoes are much smaller and
shorter lived than hurricanes because
there is not a long-term source of
moisture for them to feed on as there
is for a hurricane over warm sea.
Typically, they last on the order of a
few minutes to ½ hour.
56
Local Storm: Tornado
• Typically, the extent of a tornado is of
the order of 100 m to 500 m across at
ground level.
• The Fujita scale serves a similar
purpose for Tornadoes as does the
Saffir-Simpson scale for hurricanes. It
measures the strength of the Tornado
by the damage it does and has
associated with it wind speed ranges.
• NOAA’s National weather service
• https://www.spc.noaa.gov/efscale/
• Adapted by NBCC
• https://www.canada.ca/en/environme
nt-climate-change/services/seasonalweather-hazards/enhanced-fujitascale-wind-damage.html
Tornado at downtown Miami (courtesy of Dr. P. Irwin)
57
Local Storms: Tornado EF (Enhanced Fujita)
Scale
EF
0
EF
1
EF
2
EF-Scale Wind Speed
EF Rating
By NOAA
[mph]
By Environment Canada
[km/h]
0
65-85
90-130
1
86-110
135-175
2
111-135
180-220
3
136-165
225-265
4
166-200
270-310
5
Over 200
315 or more
EF
3
EF
4
EF
5
Source: https://en.wikipedia.org/wiki/Enhanced_Fujita_scale#cite_note-EF_SPC-9
58
Local Storms: Schematic of Tornado
(Bezabeh et al., 2018)
•
Geometric: 𝑎 =
•
Kinematic: 𝑆 = [
•
Dynamic: 𝑅𝑒 =
, 𝑟=𝑟 ,𝑣 ≈0
.
]
= [
𝚪
]
59
60
How do we simulate in laboratory
WindEEE Schematics
61
WindEEE Dome at Western
62
63
64
Local Storms: Downbursts
Flow structure of a microburst
Letchford, C.W. and Chay, M.T., 2002. Pressure distributions on a cube in a
simulated thunderstorm downburst. Part B: moving downburst
observations. Journal of Wind Engineering and Industrial Aerodynamics, 90(7),
pp.733-753.
65
Local Storms: Downbursts
66
Local Storms: Downbursts
67