The atmosphere is in constant motion. Motions are caused by and subject to a number of different forces. In this clip we will examine the fundamental forces involved in atmospheric motion.
I will also point out a few important theoretical applications of forces in equilibrium
to understand the first force that I will talk about let's look at two columns A and B. both stretching from the Earth's surface to the top of the atmosphere.
If the positive X. direction is to the right. Then the distance D. X. between the two columns equals X. B. minus X. ray.
If column A contains more mass than column B. then the surface pressure P. A is higher than P. B.
there is now a difference in surface pressure delta P. between the columns
delta P. equals P. B. minus P. A and this difference is negative in this case
now the pressure gradient in the X. direction is given by D.P. D. X. which is approximated by delta P. divided by Delta X.
the pressure gradient is a measure of the change in air pressure per unit length.
In our case P. B. is smaller than P. A so delta P. is negative. And D P D X is also negative
it means that in this case pressure is decreasing in the positive X. direction.
Similar formulas can be derived for the wind direction
suppose that we have a cube of air resting on the surface the sides of the cube all have a surface area a.
The pressure on a side multiplied by the area gives the force acting on that side of the cube.
If as before the pressure on the left peat A is higher than the pressure on the right P. B. then there is a net force on the cube directed in the positive X. direction.
This force is called the pressure gradient force F.P.
F.P. is positive because it is acting in the positive X. direction therefore F. P. equals minus the area multiplied by the pressure difference
rearranging this equation
shows that the pressure gradient force in the X. direction equals minus the volume multiplied by the pressure gradient
the minus sign indicate that if the pressure gradient D.P. D X.
Is negative as in this case the force is positive
meaning pointing in the positive X. direction
in summary the pressure gradient force drives air from high to low pressure areas.
In this example ice of ours are plotted on the map of Europe. A low pressure area is located over Ireland
and high pressure is to the south over the Atlantic Ocean
the pressure gradient is a vector with components D P D X and D P D Y And is indicated by the arrows
the arrows are pointing to the higher pressure
the pressure gradient is perpendicular to the isobars
and is strongest where the ice of ours are closer together
this figure shows the same situation for the pressure gradient force.
Now we see that the arrows are pointing in the opposite direction that is from the high to the low pressure area.
Remember the minus sign in the equation
similar to the pressure gradient the pressure gradient force is perpendicular to the isobars.
And is strongest where the isobars are close together
the second important fundamental force is a result of the rotation of the earth around its axis. From West.
To East
any object on earth is rotating as well and therefore has a high rotation velocity from west to east. We are not aware of this velocity as we only notice motions relative to the rotating earth
in higher latitudes the rotation velocity is lower.
Because the size of the latitude circle is smaller
now suppose that an air parcel moves from point A to point a prime on a certain latitude to the north
if the earth was not rotating the air parcel would arrive at a point a prime somewhere on the border between Spain and France
however the earth is rotating which is indicated by the green area
if the parcel was not moving northwards it would have moved from point A to B. with a certain rotation velocity indicated by the Green Arrow
similarly air parcel to at location a prime would have moved to be prime with a lower rotation velocity indicated by the yellow arrow. Now if air parcel one is moving northwards it keeps its rotation velocity due to the conservation of momentum.
Consequently it does not arrive at a point to be prime.
But at point C. somewhere in Italy.
So ere parcel one has an eastward displacement relative to Earth.
For an observer on Earth air parcel one is displaced to the right this displacement is attributed to what we call the Coriolis force
for an air parcel moving from north to south a similar argument applies if the earth was not rotating an air parcel starting at point A would arrive at a point a prime
but now it keeps its lower rotation velocity when moving southwards.
Consequently it does not arrive at point B. prime.
But at point C..
So the air parcel has a westward displacement relative to the earth
for an observer on earth the air parcel is again displaced to the right
as you can see here.
The displacement is to the left in the Southern Hemisphere
as observed from over the North Pole the earth is rotating counter clockwise.
The earth has completed exactly one full rotation when the green arrow.
Is pointing in the same direction again.
This takes twenty three hours fifty six minutes and four seconds and this period is called a sidereal day. However due to the orbit of the earth around the Sun The Green Arrow does not point towards the sun any longer.
There is now still a small angle left that the earth needs to turn in order to bring the green arrow back so it is pointing directly at the sun
on average this takes an additional three minutes and fifty six seconds.
So after twenty four hours the arrow points to the sun again indicated by the blue arrow
this period is called a mean solar day.
To calculate the rotation rate of the earth Omega we must use the sidereal day length which gives us a value of seven point two nine two multiplied by ten to the minus fifth power per second we will use this value in all subsequent calculations
the rotation on the local horizontal plane has a maximum value at the North Pole where it equals Omega
but at a certain latitude five the rotation rate is equal to a mania multiplied by the sign of the latitude
at the equator the rotation of the earth produces no rotation on the local horizontal plane
this can also be seen from the equation using zero for the latitude since the sign of zero equals zero
hence without further duration here is the expression for the Coriolis force
it is the mass M. multiplied by the wind speed v multiplied by twice the rotation rate of the earth Omega and the sign of the latitude
the equation is usually written using this so-called Coriolis parameter F. where F. equals two multiplied by Omega multiplied by the sign of a latitude
notice that at the North Pole where the latitude is ninety degrees the Coriolis parameter has a maximum value. Whereas on the equator it equals zero
Moreover it is important to know that the Coriolis force is proportional to the wind speed
is perpendicular to the wind direction.
And points to the right in the northern hemisphere
suppose that we draw the eyes of ours parallel and straight As in this situation.
With a lower pressure to the north.
Then the pressure gradient force on an air parcel is pointing to the north.
Now if the Coriolis force is equal but opposite to the pressure gradient force the two forces will cancel each other out
the air parcel that is some ject to this Coriolis force is said to be moving with the deer's terrific wind speed.
This situation is called geo strategic equilibrium
it is obvious that the geostrategic equilibrium only exists if the isobars are straight and parallel and if there are no other forces acting on this air parcel
from the expression for the equality of the two forces we can derive an expression for the juice trophic windspeed.
It produces this expression for you G.
and A similar one for V G.
We are now able to calculate the wind speed from a given pattern of isobars
Let's take a look at the behavior of the geostrategic wind blows parallel to the ice of ours
Furthermore the low pressure area is located to the left of the geostrategic wind.
And finally the strength of the geostrategic wind depends on the eyes of our distance the closer the isobars the higher the wind speed.
The geostrategic wind is a good approximation of the real wind usually correct to within ten percent of the actual wind.
Instead of using isobars on a surface of constant height it is also possible to use a surface where the pressure is a constant This is called a pressure surface.
A pressure surface will usually be slightly tilted just like the five hundred hectare best surface in this example.
On a pressure surface lines of equal height can be drawn the so-called iso hips is. At the intersection of the pressure surface and the five thousand six hundred meter height surface.
You can find the five hundred and sixty Deca meter iso hips.
Other iso hips as can be drawn as well of course
now the G.S. trophic wind is blowing parallel to the eye so hip says.
With a low pressure and the low heights to the left
here you can see the same situation with the iso hits is indicated in red.
From the equations for the Jews traffic wind at height levels.
And the equation of hydrostatic equilibrium. We can derive the expressions for the geostrategic wind on a pressure surface
note that we now have a height gradient instead of a pressure gradient. And density has disappeared from these equations which is a great advantage
let's compare the real wind with a geo strategic wind here on the eight hundred and fifty ecto Pascal surface the real wind is indicated by the green arrows.
And the geostrategic wind by the Red Arrows
close inspection reveals that the geostrategic wind is almost equal to the real wind
one reason that the geostrategic wind differs from the real wind is that other forces are not taken into account.
For instance close to the surface friction becomes important.
Friction is acting in the direction opposite to the velocity
it will slow the air parcel down. And therefore the Coriolis force will be smaller
the pressure gradient force is not affected by friction and remains unchanged.
Thus the wind velocity will not only be reduced but will also turn towards the low pressure area and will result in a smaller Coriolis force and an unchanged pressure gradient force is a net force towards the low pressure
a new equilibrium will be formed in which the three forces pressure gradient friction and coriolis cancel each other out
this new equilibrium is not geostrategic any more. The wind will cross the isobars at a certain angle towards the low pressure and away from the high pressure. It is the ultimate reason that mid latitudes cycle and and anti Cyclons dissipate and vanish in time.