Geostrophic wind vs pressure gradient question

[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