Geostrophic wind vs pressure gradient question

[GIVMI55W]

Hi all,

I am new and I hope this is the correct forum :)

Question1:

Geostrophic wind = equilibrium of forces between Coriolis, pressure gradient and centrifugal force. According to picture 1, the Coriolis opposes the gradient force. This is the case because the Coriolis is always acting to the right (NH) to the wind direction.

If we now bring the friction into the game, the pressure gradient force remains the same, whereas the wind force and therefore the Coriolis decrease. The wind should turn to the left (surface wind), picture 2.

The point where all 4 forces act is the small blue circle on the picture and I now imagine that the wind and Coriolos force decrease, the pressure gradient (which has the same force as without friction) should pull the small blue circle upwards and therefore move the wind arrow to the right?? But according to picture 2, it moves to the left??

WHY ? :ugh: Where is my error in reasoning?

Question 2:

Is the Coriolis force only opposing the pressure gradient when we are looking at the geostrophic wind?

The guy in the video (https://www.youtube.com/watch?v=7zSN18isTYk) explains the cyclonic and anticyclonic flow. But in his explanation, the Coriolis force is in a right angle to the pressure gradient??? It should be in a right angle to the wind. At least this should be true for the geostrophic wind. What is the difference?
The wind should be blowing parallel to the isobars, in his video, it is blowing across? This should only be the case for lower winds with friction?

Thank you very much for your help.

[GIVMI55W]

Hi,

thank you very much for your post, but it unfortunately didn't answer my questions :/

(1) I already knew that the wind is moving into the low, but I didn't understand why. Picture 2 shows clearly that the wind turned to the left. But why? When I imagine the wind and therefore the Coriolis becoming smaller because of the friction force, the long arrow (pressure gradient force) should move the tail of the arrow up -> so the wind should turn to the RIGHT. The Do you understand what I mean?

(2) Is the Coriolis opposing the pressure gradient (like in picture 1) or is it perpendicular to the pressure gradient, like in the video ?(https://www.youtube.com/watch?v=7zSN18isTYk) The video is called surface wind direction (no friction) so I thought it is without friction :)

Best,

GIVMI55W

[Martin_123]

I think you're forgetting centripetal force in the low.
Have a look at this page - 7(n) Forces Acting to Create Wind (http://www.physicalgeography.net/fundamentals/7n.html)

Coriolis effect simply makes stuff to deflect right in NH. The diagrams you are looking at are confusing, the coriolis force really acts in the same direction as the blue arrow in the first picture

[Martin_123]

you're right EGQL1964, the centripetal effect might be tiny in this situation. The main thing here is that once the air parcel gets closer to the low (or further from the high) the centrifugal (which is not even shown in OPs pictures) and coreolis effects will lessen, but the pressure gradient force will still remain strong. Thus your parcel starts to deflect towards the center of the low (or "left" as the OP puts it)

[gfunc]

Meteorology person here:

First of all a few things that seem to have become confused along the way (and persists in some Aviation text books)

Geostrophic wind is the wind that results from the pressure gradient force being exactly balanced by the Coriolis force - this can only occur in the absence of friction and along straight isobars, i.e. when there is no contribution from centripetal force. [so Question 2 - Yes]

Gradient wind is the geostrophic wind with the centripetal force from flow around curved isobars included. This extra force results in flow around ridges being faster than the geostrophic wind - in the question above we are looking at straight isobars, so the centripetal force is a red herring here.

The actual wind is the gradient wind plus the friction force, which directs it towards low pressure centres near the Earth's surface.

For the first question, I think the confusion of the original poster is thinking of the wind in the pictures as a force - it is not, it is the resultant motion from all the other forces. Picture one is really unhelpful here as it shows an out-of-balance picture that sort of mimics the force balance pictures you see in POF. The best place to start thinking about this is by remembering that Coriolis force always acts at right angles to the motion of the air parcels (to the right in the Northern Hemisphere) and the size of this force changes only with speed of the air parcel. Now, imagine an air parcel at rest is suddenly subjected to the pressure pattern shown in the first picture with no friction. It will accelerate toward the low pressure at the top of the picture and as it does so the Coriolis force will increase with speed and continually pull the parcel to the right, resulting in a path that curves to the right until the air parcel reaches a speed where the PGF an Coriolis force are exactly balanced and the parcel is moving along the isobars - we have geostrophic balance.

If we take take this balanced situation with air flowing happily toward the East along the isobars and suddenly add in some friction (this instant is shown in picture one), the first thing that happens is that speed of the air parcel drops and the Coriolis force is reduced. Now the forces are no longer balanced and the PGF wins out and the parcel accelerates toward the low pressure region (i.e. is now moving toward the ENE in the picture). The northerly component of motion increases, which increases both friction and Coriolis force until there is a balance between the three forces acting in the north-south direction. At this point the air is balanced and flowing slightly across the isobars, towards the low centre.

I would say the key here is to remember that friction is always opposite to the direction of motion and the Coriolis is always at right angles to it. Then if you break the three forces into their N-S and E-W components you can convince yourself that the net sum is zero - not a trivial thing to do, but you can sort of see in picture two that the E-W component of the friction force is equal and opposite to the E-W component of the Coriolis force and that the sum of the N-S components of these is equal to the PGF.

Hope this helps!

G

[Alex Whittingham]

A perfect summary - thank you. One postscript; textbooks written for the EASA ATPL will usually refer to centrifugal force rather than centripetal and that makes force diagrams for airflow around curved isobars look different from 'standard' textbooks. It is, unfortunately, impossible to convince EASA that their usage of the term is misleading and they ask questions such as:

Q.At the same latitude the geostrophic wind is less than the gradient wind around an anticyclone with equal pressure gradient because the:

(A) Centrifugal force is added to the pressure gradient
(B) Centrifugal force opposes the pressure gradient
(C) Effect of coriolis is added to friction
(D) Coriolis effect opposes the centrifugal force

[paco]

And that's the problem isn't it - all the schools are torn between telling the truth and what EASA want to hear.

Phil

[gfunc]

Just to clarify: Centrifugal force is the correct term (the particles are apparently being flung outward as they travel along a curved path). However, the way the equations (and therefore technical books) are written the relevant term is called the centripetal acceleration, (e.g. AMS Glossary (http://glossary.ametsoc.org/wiki/Gradient_wind) ), so I've made the schoolboy error of confusing the names! My apologies for that.

G

[Alex Whittingham]

I think you were right first time! Centripetal force is required to keep objects following a curve. Centripetal force is an actual force, centrifugal force is only an apparent force, really an effect of Newton's first law.



but Coriolis force is only an apparent force as well. Oh dear.

[paco]

I won't mention cyclostrophic force then... :)

Phil