On vorticity

I’ve promised a long time ago to write a post on vorticity (Hallo Geli! :-)). So here it comes!

Vorticity is one of the concepts in oceanography that is often taught via its mathematical formulation, and which is therefore pretty difficult to grasp for those of us with less mathematical training. But it’s also a concept that you can have an intuitive grasp of, and I’ll try to show you how.

The easiest way to imagine what “vorticity” is, is to think of a little float in a flow. In a vorticity-free flow, that little float will always keep its orientation (see below). However if there is a shear in the flow, i.e. the flow field carries vorticity, it will start to turn.

Flow fields without vorticity (top) and with vorticity (bottom).

This even holds true for vortices: There are vorticity-free vortices as well as those that carry vorticity (as the name “vortex” would suggest).

Vorticity-laden and vorticity-free vortex. In the left plot, angular velocity of all particles is the same. In the right plot, angular velocity increases the closer you get to the center of the vortex.

If you think back to the discussion on a tank spinning up to reach solid body rotation, you might recognize that only the vortex with vorticity moves like a solid body. To me, a solid body is basically a fluid with so much friction in it, that molecules cannot change their position relative to each other. And that serves as my memory hook for one condition for the formation of vorticity – the flows must have viscous forces and friction in it.

This sounds very theoretical, but there are a lot of instances where you can spot vorticity in real life, for example twigs caught up twirling in eddies at the edge of streams are clearly moving in a vorticity-filled environment. Below, for example, the stream is clearly not vorticity-free.

Did this help a little? Or what else might help?

On drawing on the board by hand in real time

Drawing by hand on the board in real time rather than projecting a finished schematic?

It is funny. During my undergrad, LCD projectors were just starting to arrive at the university. Many of the classes I attended during my first years used overhead projectors and hand-written slides, or sometimes printed slides if someone wanted to show really fancy things like figures from a paper. Occasionally people would draw or write on the slides during class, and every room that I have ever been taught in during that time did have several blackboards that were used quite frequently.

These days, however, things are differently. At my mom’s school, many classrooms don’t even have blackboards (or whiteboards) any more, but instead they have a fancy screen that they can show things on and draw on (with a limited number of colors, I think 3?). Many rooms at universities are similarly not equipped with boards any more, and most lectures that I have either seen or heard people talk about over the last couple of years exclusively use LCD projectors that people hook up to their personal laptops.

On the one hand, that is a great development – it is so much easier to show all kinds of different graphics and also to find and display information on the internet in real time. On the other hand, though, it has become much more difficult to talk students through graphics slowly enough that they can draw with you as you are talking and at the same time understand what they are drawing.

Sketch of the mechanisms causing westward intensification of subtropical gyres – here the “before” stage where the symmetrical gyre would spin up since the wind is inputting more vorticity that is being taken out by other mechanisms.

The other day, I was teaching about westward intensification in subtropical gyres. For that, I wanted to use the schematics above and below, showing how vorticity input from the wind is balanced by change in  vorticity through change in latitude as well as through friction with the boundary. I had that schematic in my powerpoint presentation, even broken down into small pieces that would be added sequentially, but at last minute decided to draw it on the whiteboard instead.

Sketch of the mechanisms causing westward intensification of subtropical gyres – here the “after” stage – the vorticity input by wind is balanced by energy lost through friction with the western boundary in an asymmetrical gyre. Voila -your western boundary current!

And I am convinced that that was a good decision. Firstly, drawing helped me mention every detail of the schematic, since I was talking about what I was drawing while drawing it. When just clicking through slides it happens much more easily that things get forgotten or skipped. Secondly, since I had to draw and talk at the same time, the figure only appeared slowly enough on the board that the students could follow every step and copy the drawing at the same time. And lastly, the students saw that it is actually possible to draw the whole schematic from memory, and not just by having learned it by heart, but by telling the story and drawing what I was talking about.

Does that mean that I will draw every schematic I use in class? Certainly not. But what it does mean is that I found it helpful to remember how useful it is to draw occasionally, especially to demonstrate how I want students to be able to talk about content: By constructing a picture from scratch, slowly building and adding on to it, until the whole theory is completed.