In Atmospheric Circulation – Part One we saw how the pressure “slopes down” from the tropics to the poles creating S→N winds in the northern hemisphere.
In The Coriolis Effect and Geostrophic Motion we saw that on a rotating planet winds get deflected off to the side (from the point of view of someone on the rotating planet). This means that winds flowing from the tropics to the north pole will get deflected “to the right”.
Strange things happen to fluids in rotating frames. To illustrate let’s take a look at Taylor columns.
The static image is quite beautiful, but the video illustrates it better. Compare the video of the non-rotating tank with the rotating tank.
Now to stretch the mind we have a rotating tank with an obstacle on the base – in this case a hockey puck. The height of the puck is small compared with the depth of the fluid. The fluid flow has come into equilibrium with the tank rotation.
We slow down the rotation slightly. We sprinkle paper dots on the surface of the water. Amazingly the dots show that the surface of the fluid is acting as if the puck extended right up to the surface – the flow moves around the obstacle at the base (of course) and the flow moves “around” the obstacle at the surface. Even though the obstacle doesn’t exist at the surface!
Take a look at the video, but here are a few snapshots:
This occurs when:
- the flow is slow and steady
- friction is negligible
- there is no temperature gradient (barotropic)
Under the first two conditions the flow is geostrophic which was covered with examples in The Coriolis Effect and Geostrophic Motion.
And under the final condition, with no temperature gradient the density is uniform (only a function of pressure).
Now let’s look at an experiment with a “cold pole” and “warm tropics”:
Even better - take a look at the video.
This experiment shows that once there is a N-S temperature gradient the E-W winds increase with altitude.
Which is kind of what we find in the real atmosphere:
Why does this happen? I found it hard to understand conceptually for a while, but it’s actually really simple:
So the ever increasing pressure gradient with height (due to the temperature gradient) induces a stronger geostrophic wind with height.
Here is an instantaneous measurement of E-W winds, along with temperature in a N-S section:
The measurement demonstrates that the change in E-W wind vs height depends on the variation in N-S temperature.
The equation for this effect for the E-W winds can be written a few different ways, here is the easiest to understand:
∂u/∂z = (αg/f) . ∂T/∂y
where ∂u/∂z = change in E-W wind with height, α = thermal coefficient of expansion of air, g = acceleration due to gravity, f = coriolis parameter at that latitude, T = temperature, y = N-S direction
It can also be written in vector calculus notation:
∂u/∂z = (αg/f)z x ∇T
where u = wind velocity (u, v, w), z = unit vector in vertical
In the next article we will look at why the maximum effect in the average, the jet stream, occurs in the subtropics rather than at the poles.
Meteorology for Scientists and Engineers, Ronald Stull, 2nd edition – Free (partial) resource
Atmosphere, Ocean and Climate Dynamics – An Introductory Text, Marshall & Plumb, Academic Press (2008)