Welcome back to Sports and Building Aerodynamics.
In the week on basic aspects of fluid flow.
This is the last module in this week, and in
this module, we're going to focus on the atmospheric boundary layer.
We start again with the module question.
The atmospheric boundary layer is the layer where the atmosphere is directly
influenced by the surface of the earth, by friction and by thermal effects.
Then, which statement is correct?
A, the atmospheric boundary layer is higher during the day than at night.
B, the atmospheric boundary layer is equally high during day and night.
Or C, the atmospheric boundary layer is
higher during the night than during the day.
Please hang on to your answer.
We'll come back to this question later in this module.
At the end of this module, you will
understand some basic aspects about the atmospheric boundary layer.
You will understand the concept of neutral stratification, the typical profiles of
mean wind speed and turbulence intensity in the neutral atmospheric boundary layer.
And you will understand how aerodynamic
roughness length can be practically estimated.
There are some important references that I would like to mention here.
This is not a complete list, but this is definitely recommended
reading material, provided here in a reverse chronological order.
So in the main part of this module we will
focus on the so-called neutral atmospheric boundary
layer flow over a uniformly rough level surface,
and typical mean wind speed profiles are indicated here.
This is a drawing by Davenport from 1967.
So, let's first define this atmospheric boundary layer.
Well, this atmospheric boundary layer is also sometimes called planetary
boundary layer, and it's the lowest part of the
atmosphere, which actually forms due to the direct interaction between
the atmosphere and the underlying surface, which can be land or sea.
And the time scales involved are one day or less.
So, actually, the atmospheric boundary layer is the
lowest part of the troposphere, and the troposphere
is indicated here in this graph as the
yellow layer, where the air temperature decreases with height.
So, actually, this boundary layer is a very thin shell around the earth.
The depth can range between about 100
meters and three kilometers, so this is
only 0.01% of the earth radius approximately,
and it varies substantially in space and time.
Temperature and mean wind speed and turbulence intensity
also very substantially, not only with height, but
also as a function of time, and it is very different from the free atmosphere above.
And the surface forcing that is present is friction and/or heat fluxes,
which can be heating of the atmospheric boundary layer or cooling it down.
What happens during the day actually when you have a clear
sky, then the earth surface is heated up by the solar radiation.
Then the heated earth surface actually heats the boundary layer.
Actually that heating occurs from the bottom upwards.
So that is mainly heating due to convection.
And that is then called unstable stratification,
because the hot air will rise and cold air will go down again.
It will be heated and so on.
And then you can get large vortical structures occurring in the atmosphere.
On the other hand, during the night
with a clear sky, the earth's surface will cool down substantially.
Then you have the cooling of the atmospheric boundary
layer, occurring from the bottom, and then you will have
the coldest layers at the bottom and the hottest
layers at the top and that is called stable stratification.
So, in unstable stratification, the
turbulence will be augmented by the thermal
effects, and in unstable stratification, it
might be suppressed by the temperature gradients.
And then another characteristic of atmospheric boundary layers is that you have the clouds
there, typical examples are fair weather cumulus,
stratocumulus, and fog that can be present.
Then what are the characteristics, or how can you define this boundary layer?
Well, it is actually very similar to Prandtl's concept of the boundary layer.
Although, this is a boundary layer here that we are dealing with
that has much larger scale. So it is a layer, in which the fluid
speed increases from zero near the surface to a maximum,
and almost constant value, at the top of the boundary layer.
And this height is called gradient height and the wind
that occurs there is often called the geostrophic wind.
And again, this drawing at the bottom
indicates for different terrain types how the wind
speed increases from zero at the surface to
a certain constant value at a larger height.
There are some particular characteristics that make the
ABL, atmospheric boundary layer, very different from the free atmosphere.
Let's focus on a few of them.
Depth, for example.
For the atmospheric boundary layer, this ranges
between 100 meters and about three kilometers,
varying in space and time therefore, and diurnal
variations can be very pronounced over land.
In the free atmosphere, this depth is much less variable and
ranges between 8 and 18 kilometers, so variations are much lower.
Concerning mean wind speed, well, this is near-logarithmic in
the surface layer, and nearly geostrophic in the free atmosphere.
Turbulence in the atmospheric boundary layer is present over the entire
depth while it is very low to absent in the free atmosphere.
Vertical transport in the atmospheric boundary layer
is turbulence dominated while in the free atmosphere, actually,
you have slow vertical transport, and this is by the mean wind flow that it occurs.
And finally, dispersion in the atmospheric boundary layer is rapid
in vertical and horizontal direction, due to turbulent mixing, while
in the free atmosphere, this occurs by molecular diffusion, and
rapid horizontal transport can occur by the mean wind.
Let's then briefly look at how the
atmospheric boundary layer can vary throughout the day.
We focus on clear-sky conditions here, and first we look at the night, during the
night, as mentioned before, the earth surface cools
down by long wave radiation through the sky.
So, the boundary layer actually receives a generally stable stratification.
So, we get the quite shallow nocturnal boundary layer.
The depth of this boundary layer depends on wind velocity and
surface roughness because when they both increase the depth of the boundary
layer will increase and the air above this nocturnal boundary layer
is slightly stratified, due to heat loss to space during the night.
Then when the day starts, and the sun comes up and starts shining and
heats up the earth's surface by
short wave radiation you get convective motions then
that become quite important, especially at relatively
low to moderate wind speeds, so you
get large convective dominated turbulence, in
fact, actually, in this unstable atmospheric boundary layer.
And you will also have a surface layer developing, where more or less, there's
more or less an equal share of
wind induced and thermally induced, convection induced turbulence.
Except when you're dealing with high wind speed,
then the wind induced turbulence will be more pronounced.
But we'll focus on that later.
And then, night sets in again, well, sun set
first, of course, stops heating the atmospheric boundary layer.
And then, we get the development of a new
nocturnal boundary layer, and the cycle starts all over again.
So, what about strong winds, and this is quite important.
Well, in strong winds, the thermal effects are generally negligible.
This certainly holds for this surface layer.
And this is actually the very important and
basic aspect on which almost all wind tunnel testing
in sports and building aerodynamics is based but
also many computational simulations of the atmospheric boundary layer.
So, let's turn back to the module question then.
Which of these statements is correct?
Well, because the depth of the boundary layer increases
with the convective thermal motion and this is more pronounced
during the day, the right answer is the atmospheric boundary layer
is higher during the day than at night.
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Let's look at a few spatial scales.
These are the well-known meteorological scales varying from the
synoptic scale down to the mesoscale, and finally, the meteorological microscale.
Synoptic scale is the scale of the largest cyclones, then you have the mesoscale,
where weather systems such as a mesocyclones,
orographic effects and land-sea breezes occur, and then
down to the microscale, where we have
small cloud structures, mixing and dilution, heat and
mass transfer between building, soil, vegetation,
and the atmospheric boundary layer and so on.
And these are some examples of
computational simulations at the meteorological microscale,
where also details of buildings and
topography are typically taken into account.
But apart from these scales, if you focus on building
physics and building aerodynamics, actually, we have some other scales.
We can go further down from these well-known
meteorological scales down to the building scale, the
building component scale, which are roofs, facades, and
floors, and even down to the building material scale.
And for each of these scales, actually, there are dedicated computational models.
The mesoscale meteorological models for the mesoscale.
Microscale meteorological models, also called
CFD, for the meteorological microscale.
At the building scale, you have building energy simulation models, and at the
component scale, we have the so-called, building
envelope heat air moisture transfer models, BE-HAM.
What we will focus on in this MOOC is the meteorological micro-scale.
And this is actually a very nice diagram that shows, actually,
the scales of atmospheric phenomena for different types of atmospheric phenomena,
where you can see the spatial scales indicated from 10 centimeters
to 10,000 kilometers and temporal scales from one minute to 10 years.
And what we will focus on this MOOC is actually this part.
This is the meteorological microscale, where we deal with
turbulence, where we deal with thermals, building wakes, and convection.
If you have a neutral atmospheric boundary
layer over uniformly rough level terrain, as indicated
here, then the wind speed generally
increases with height in a logarithmic fashion, and
turbulence intensity decreases with height because the
largest production of turbulence occurs at the surface
due to the friction with
the elements on the surface, so with the roughness.
So, if the thermal processes are absent or negligible, the
atmospheric boundary layer is called neutrally stratified, and then the
wind speed can be described, by this called log law,
or the power law, the mean wind speed that is.
So, the log law is indicated on the left
side here where you have the friction velocity,
kappa the von Karman constant, z the height above
ground level, and z nought is the aerodynamic roughness length.
The other equation is the power law.
Actually, both equations give very similar profiles.
In the power law, you see a reference wind speed; you also
see a reference height, and you see the so-called power law exponent.
So, roughness of the surface in these equations is taken
into account by either the aerodynamic roughness length or the power law exponent.
So, how can, then, if you want to use one of these
profiles, how can you determine this
aerodynamic roughness length or this exponent?
Well, therefore roughness classifications have been devised,
that actually give these values for different
types of terrain, be it rough sea, prairie land, forest, suburbs, or city centers.
And this is a classification made by Davenport.
And later on, this classification was updated by
Wieringa, and this publication was launched in 1992.
Where you see, actually, that the atmospheric roughness length here varies from 0.2
millimeters for open sea or ice or a very flat, smooth surface.
Up to a value of two or a bit larger for centers of large cities.
What is important to note here, is that this aerodynamic roughness length is
by no means a representation of the actual height of the obstacles because
in centers of large cities, you have very tall buildings, which, of course,
have a much larger height
than indicated by this aerodynamic roughness length.
What is important, if you want to assess aerodynamic roughness length, is that
you do that for quite a large distance upstream of the site of interest.
And the reason for that is that when an atmospheric
boundary layer develops over terrain, it takes quite some
distance for this development of the boundary layer to establish
itself to the height, to a given height above the surface.
So, an example of an estimation of aerodynamic
roughness length, based on terrain type is given here.
And often this estimation is not very easy
because you have different types of terrain that occur
in patches, actually, upstream, and you just have
to try to get the best estimate based on that.
Some important comments here related
to these equations because these laws are strictly
only valid over uniformly rough terrain, but in
reality, of course, the terrain is never uniformly rough.
This log law and the power law
are definitely not valid for a flow around
individual elements and obstacles, because then the flow patterns
are much more complex, as you will see later.
So, it's only an average representation of the wind speed over rough
terrain and only starting from a certain height above the highest obstacle.
What is also important is that it describes
a profile that is formed, after having experienced the
fetch of terrain upstream of your site of interest
of at least 5, but up to 10 kilometers.
These are some typical profiles of dimensionless mean speed and turbulence
intensity, where indeed turbulence intensity,
you see, clearly decreases with height.
And then we can focus on what happens with
roughness changes, because roughness changes,
in reality are everywhere whether
the flow transitions from an ice surface to a
build surface to a city surface, or a suburban terrain.
You will get a so-called development of internal boundary layers.
This is an example here where we focus
on the atmospheric boundary layer that flows over
a grass-covered terrain, then reaches the shore and
then will adapt to the smoother sea surface.
So this is a graph that shows the
logarithmic wind speed profile over the grass surface.
And at point O, we have the shore, so the coastline, and then
you see the height of the internal
boundary layer indicated with these curved lines.
So, the height develops as the boundary layer flows further over the sea surface.
And what you see, actually, at the bottom here, is that due
to the lower roughness, this profile will now start accelerating at
the bottom and the old profile, over the land surface is given
by the dotted line and the new profile by the solid line.
However, at the top, it will take some
time for this development, for this acceleration to
also be felt at the top, and this occurs due to upward exchange of momentum.
There are quite some equations that have
been developed to determine the atmospheric boundary layer height.
This is just one of them, and what is interesting
here in this equation is that you see that you
need a downstream distance of 1.7 kilometers, only for the
internal boundary layer to reach a height of 100 meters.
This is quite a large horizontal distance that is needed.
Let's briefly focus on wind velocity
measurements in the atmospheric boundary layer
and we need to define standard
measurements because we know wind speed increases
with height, so it's important that when we report wind speed, we
also report the height at which it has been measured.
And this is set at a height of 10 meters above
ground level, so this is set by the World Meteorological Organization.
Standard measurements are mean horizontal speed and wind direction.
Be careful, the wind direction is the direction from which
the wind blows, not the direction in which the wind is blowing.
Then there are important aspects to be considered in
terms of time resolution and averaging and reporting intervals.
If you want to accurately measure also turbulence, well, you have
to go down to a much finer resolution than one Hertz.
But if you are focusing on mean wind speed, then
one minute to one second interval is actually quite fine.
If you want to average those wind speed
values when you are processing them and reporting
them, well, then it's best to look at
averaging intervals from 10 minutes to one hour.
And the reason for that is the wind speed power spectrum of Van der
Hoven and that actually indicates the power
indeed associated with different periods, so cycles.
What you see here is that there is clearly a large
amount of atmospheric changes associated with the yearly cycles.
Also, the four day cycle because that's the time
for large weather systems to pass over the surface.
Also, the daily cycle, night-day cycle, is indicated there and also
turbulence, but between those two last peaks, you get a spectral gap.
A gap in which you will get quite stable average values.
So, indeed, it is recommended to average wind speed values over 10 minutes to one hour.
In this module, we've learned about some basic
aspects of the atmospheric boundary layer, about the
concept of neutral stratification, the typical profiles of
mean wind speed and turbulence intensity in the neutral ABL.
We have also seen how the aerodynamic roughness length can be practically estimated.
This module concludes the week on basic aspects of fluid flow.
And in this week, we've seen some
important physical properties such as density and viscosity.
We've addressed how the location of the
velodrome can determine the extent of world hour
records in cycling. We have seen how turbulent
flows can be very complex, and why
there's not yet a good definition of
turbulence, and we have focused on boundary layers, including
this special case of atmospheric boundary layer,
where sports and building aerodynamics take place.
This week has provided a lot of material in a
very short period of time, so thank you for still watching.
And this week is definitely important to
fully understand the rest of the course.
And while I think this quote remains very applicable: the
roots of education are bitter, but the fruit is sweet.
In the next week, week two, we are going to focus on wind-tunnel testing.
Thank you again for watching, and we hope to see you again in the next week.
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