At the IUTAM Symposium "Tubes, Sheets and Singularities in Fluid Dynamics" held in Zakopane (September 2001), I found it helpful, for myself if for no-one else, to compose an abstract of each lecture in the form of a limerick. Here is a selection of these limericks, some of which appeared in the Proceedings of the Symposium
When water is pushed through a hole,
The ring vortex plays a key role;
When the core is quite thin,
Res'nant waves are packed in;
To grasp them, why that is the goal!
A sheet that is stretched, in collusion
With limited viscous diffusion,
Upon a flat table,
Is grossly unstable;
But frankly, it's all a delusion.
That a vortex sheet is unstable
Was known to the people of Babel;
We find by immersion
And solve it as well as we're able.
Vorticity fields can collapse
Under Hamiltonian maps;
It may be the norm
In turbulent flows; well p'raps!
It's a matter of utmost felicity
That a vortex can change its helicity
From right- to left-handed --
See in papers expanded
My work on breakdown of vorticity.
When the strain on a tube is unsteady,
For excitable modes please be ready:
By scaling we claim
In a suitable frame
A vortex bursts into an eddy.
When driv'n by extreme agitation,
I am subject to fierce dissipation;
In each current sheet
There's created much heat,
And my field thus achieves saturation.
If seeing a third-order link
You colour it green, brown and pink,
As hills follow hollow;
So a field triply-linked cannot shrink.
If you're not too dreadfully weary,
You'll ask what's the point of this theory?
Just please recollect
That B-lines reconnect;
I hope that will answer your query!
I talk of disruptive explosion,
Which generates plasma erosion,
Swift as an arrow,
The fingers get narrow,
I present it as digit implosion.
The process of line reconnection
Results from diffusion-advection;
With a flick of the wrist
I can generate twist,
And this for your greater delection!
With a strain that's non-axisymmetric,
The dance of two whorls is quite hectic;
They pulse and converge
And eventually merge;
The whole process is quite apoplectic!
The magnetic field of the Sun
Engenders a whole lot of fun;
There's nothing to beat
Collapse to a sheet,
And that's how the heating's begun.
We measured the helical flow
In a tube at some speeds high and low;
We readily reckoned
Four meters per second
As the critical speed you should know.
Topological arguments show
That the energy's bounded below;
But what's so engrossing's
The number of crossings,
From which my new insights will flow.
We found a complexity measure --
It really is quite a treasure --
For a vortex entangled,
By methods new-fangled;
I'll explain if you have enough leisure.
Research on fields anisotropic
Is surely an interesting topic;
The unit binormal
Shows features abnormal,
As seen if you're not too myopic!
In turbulence near to a wall
There are structures much longer than tall;
With the breakdown of streaks,
The vorticity peaks;
And the speed can slow down to a crawl.
Of wavelets I'm an adherent;
Some people think me quite errant!
But like structures extracted
By techniques compacted,
My lecture's entirely coherent.
Here's a blob that's subjected to swirl;
It's a problem for somebody virile!
But right at the core
Where it turns more and more,
That's where I get in a whirl.
I'll analyse Navier-Stokes,
For dynamics of vodkas and cokes;
[A] is an entity
Near the identity;
That's how I'll baffle you folks!
I live in the boundary layer
Which I handle with exquisite care;
But near separation
There's an queer indication
Of something that shouldn't be there!
Singularity? Yes, I conceive it,
The problem is how to achieve it;
With array octahedral
Like a modern cathedral --
When you see it, you better believe it!
Mass in the cosmos is clumpy,
Sometimes it makes me quite grumpy;
I go backwards in time
By methods sublime,
To find out what makes us so bumpy.
I'll paint you a dazzling picture
Of the truth of the Maslov conjecture;
Weak singularity --
That is the gist of my lecture.
I use without any compunction
A well-chosen wavelet function;
With theorems nice,
And methods concise,
My results are immune to debunction.
Flow past a wall that is rough
Is a problem to do off-the-cuff;
When the surface is toothed,
It's effectively smoothed,
By a mapping that's complex enough.
I'll talk about quantum switchover
As felt going from Calais to Dover;
The vortex lines shift
Reconnect and then lift . . .
I'm sorry my lecture's now over!
On the problem of vortices five,
For long I've continued to strive;
Sometimes they're stable,
And then I am able
To show how they jiggle and jive.
I'll try to put it in words:
You'll think I'm away with the birds!
Turb'lence compressible --
Spectrum of decibel,
K to the minus five-thirds.