The flow of air through the atmosphere is not always smooth and steady sometimes the airflow becomes erratic and unsteady the flow is then said to be turbulent.
A good example of this turbulence occurs in the layer of air close to the ground.
Strong turbulence during the daytime can cause this layer of air to grow to a height of one to two kilometers with small clouds forming on the top.
In this clip we will take a closer look at turbulence its origin and description I will also discuss the vertical fluxes that it generates
turbulence can also be found on a much smaller scale take these two examples here.
It is obvious that steady and straight laminar flow may suddenly become fluctuating and chaotic turbulent flow
turbulence is also visible in a time series of wind speed
large fluctuations may occur on short and long time scales
fluctuations in the wind can also happen on spatial scales as you can see here in the irregular patterns caused by the fluctuating wind moving over a field of barley
turbulence will induce the same behavior in other quantities as well.
If air temperature is measured with a rapid responding thermometer the readings will also show and irregular and chaotic pattern.
So we can see that turbulence occurs in both time and space.
It occurs on many scales from seconds to hours and from centimeters to kilometers
usually turbulence can be generated by two mechanisms. The first mechanism is called mechanical production the flow becomes turbulent due to an obstacle such as the cylinder in this picture.
The steady laminar flow coming from the left has to find a way around the cylinder and the straight flow is deflected sideways.
The flow becomes unsteady as more and more layers are perturbed by the air parcels being pushed out of the way by the obstacle and the other air parcels. The flow to the right of the cylinder has become turbulent. The mechanical generation of turbulence can be clearly seen in these animations.
In both animations a laminar flow is coming from the left
in the upper animation the airflow has to find its way around a small cylinder and thus becomes turbulent.
And the lower animation the air flows over the hills and becomes turbulent when it encounters the valleys
the second mechanism which generates turbulence is called thermal production thermal production of turbulence can be visualized by a special photographic technique where colors denote density gradients in the air.
Here you can see that if the air is heated by a soul during iron it becomes hotter than its surroundings the hot air will have a lower density
this hot air will rise and displace the air above it
the heating creates thermals and convective turbulence
This animation shows a cross-section of the lower kilometer of the atmosphere.
You can see how the air behaves on a clear and sunny day when the earth's surface is heated from below.
Red and green indicate relatively warm air.
And blue relatively cold air.
You can see rising thermals of warm air and sinking air parcels of cooler air.
These thermals generate turbulence over the whole depth of this layer
it also shows a defining characteristic of turbulence it mixes the air parcels
to describe turbulence Statistically we use what is called Reynolds decomposition
if we have a time series of a certain quantity C..
We can calculate the average sea bar over a certain time period.
It is now possible to write the instantaneous value C.
as the sum of the time average C. bar
plus a fluctuation C. prime.
By definition the time average of C. prime equals zero
for our time series of temperature T.
we can subtract the time average T. bar
and create a new time series. T. prime. With an average of zero
Now if we have to time series a prime. And be prime where both have an average of zero.
We can create a time series of their product a prime multiplied by B. prime.
Which gives an indication of the correlation between A and B..
If we take a closer look at the correlation a positive and negative correlation can be detected.
In the time slots marked in blue there is a clear anti correlation if a prime is negative then B. prime is positive. The product a prime be prime is then negative.
For the time slot marked in red there is a clear correlation. A prime and B. prime are both positive and so is their product.
Now if we calculate the average of a prime be prime we find that this average is not equal to zero.
This average is called the covariance of the two Time Series A and B..
Mathematically we can do you arrive an expression for the average of the product of a two time series A and B. as follows.
The average of a multiplied by B. is the average of a bar plus a prime multiplied by B. bar plus B. prime. Expanding the product leads to the total average of a bar B. bar.
Plus a bar be prime
plus a prime B. bar
plus a prime be prime
the average of each term can now be calculated separately.
The second and third terms are equal to zero by definition.
This shows that the average of a multiplied by B. equals the average of a multiplied by the average of B.
plus the covariance of A and to be
if we use the vertical velocity W. for A and temperature T. for B. then we get the following expression for W. multiplied by T..
If we have a measurement taken over a flat surface then the average of vertical wind speed W. bar is equal to zero.
And the first term vanishes. The second term remains and is called the turbulent sensible heat flux
multiplying the average of W. prime T. prime with the row C P We can define the sensible heat flux H
H indicates how much energy in the form of heat is transported vertically from or to the surface. Per second. And per square meter
consequently its unit is Jewel per second per square meter or watt per square meter
now I will explain how turbulent motions are able to generate a sensible heat flux using a temperature profile with temperature on the horizontal axis. And height on the vertical axis.
First let's consider a daytime situation.
The temperature decreases when moving upwards away from the hot surface. It means that D. T. over D.Z. is negative
suppose we measure the temperature and vertical velocity at the height indicated by the dotted line.
Now if a hot air parcel moves upwards.
The hot air will be detected by the thermometer once it crosses the measurement height where the average temperature is lower.
T. prime will be positive
also the positive value of the vertical velocity will be measured
so both a W. prime and T. prime will be positive and the product W. prime T. prime will also be positive it means that heat is carried upwards hence a positive sensible heat flux
now if a cool air parcel moves downwards.
The cool air will be detected by the thermometer once it crosses the measurement height where the average temperature is higher T. prime will be negative.
The negative value of the vertical velocity will also be measured at this height. So both a W. prime and T. prime will be negative but the product W. prime T. prime is still positive. It means that we have a positive sensible heat flux for both upward and downward moving air parcels
Next let's consider a night time situation. The temperature increases when moving upwards from the cool surface
it means that D.T. over D.Z. is positive
upward motion now results in cooler air reaching the measurement level T. prime is negative while W. prime is positive
the product W. prime T. prime is negative.
Downward motion results in the opposite where warmer air reaches the measurement level. T. prime is positive. While W. prime is negative
the product W. prime T. prime is still negative
it means that we have a negative sensible heat flux for both upward and downward moving air parcels
in summary due to turbulent motions the sensible heat flux is usually negative at night.
Which means that heat is transported towards the surface
the sensible heat flux is usually positive during the day.
Which means that heat is transported away from the surface
it shows that term Elance plays an active role in energy transport close to the Earth's surface. Besides heat terminal and is also able to transport other quantities such as momentum water vapor carbon dioxide and many more substances.