FLUID DYNAMICS LIMERICKS
Written by KH Moffatt during each lecture at the
IUTAM Symposium on vortex tubes, vortex sheets and
singularities
held at Zakopane, Poland, 2-7 September 2001
Shigeo Kida, Nagoya, Japan
Vortex core pressure is low,
And it's usually curved like a bow;
Computational sketching
Shows non-uniform stretching
And spirals wrapped up by the flow.
Dale Pullin, Caltech, USA
A scalar transported by flow,
In a spiral of type that we know,
Itself becomes spiral,
Possibly chiral,
And its spectrum is found without woe.
Yasuhide Fukumoto, Kyushu, Japan
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!
Robert Krasny, Michigan, USA
Vortex blob methods discrete,
Applied to roll-up of a sheet,
Will persuade any cynic
That heteroclinic
Tangles give insights quite neat.
Stephane Le Dizes, Marseille, France
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.
Cedric Brun, Madrid, Spain
Any violent turbulent storm
Contains many a wriggling worm;
We detected these creatures
And similar features,
By methods inflicting no harm.
Alberto Verga, Marseille, France
That a vortex sheet is unstable
Was known to the people of Babel;
Through total immersion
We find the dispersion,
And solve it as well as we're able.
Evgenii Kuznetsov, Moscow, Russia
Vorticity fields can collapse
Under Hamiltonian maps;
Singularities form,
It may be the norm
In turbulent flows; well p'raps!
Pavel Kuibin, Novosibirsk, Russia
Vortices coiled up in doubles
Bring great analytical troubles;
But with series of Kapteyn
We're able to obtain
Their speed, in the absence of bubbles!
Keith Higgins, Melbourne, Australia
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!
Valery Okulov, Novosibirsk, Russia
It's a matter of utmost felicity
That a vortex can change its helicity
From right- to left-handed --
See papers expanded
On my work on breakdown of vorticity.
Maurice Rossi, Paris, France
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.
Bruce Bayly, Arizona, USA
Eigenfunctions of dynamos fast
Have fine structure of gradient vast;
I ask you to gaze
At equations of phase,
And singular things that don't last.
Aake Nordlund, Copenaghen, Denemark
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.
Christoph Mayer, Bochum, Germany
If you notice a third-order link
You can colour it green, brown and pink;
Invariants follows,
As hills follow hollow;
So a field triply-linked cannot shrink.
Keith Moffatt, Cambridge, UK
If you're not too dreadfully weary,
You may ask: what's the point of this theory?
Just please recollect
That B-lines reconnect;
I hope that will answer your query!
Cowley, S.C., Imperial College, UK
I talk of disruptive explosion,
Which generates plasma erosion,
Swift as an arrow,
The fingers get narrow,
I'll present it as digit implosion.
Gunnar Hornig, Bochum, Germany
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!
Eric Priest, St Andrews, UK
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.
Xi-Lin Xie, Shanghai, China
We measured the helical flow
In a tube at some speeds high and low;
We readily reckoned
Four meters per second
As a critical speed you should know.
Peter Akhmet'ev, Moscow, Russia
The invariant of Sato-Levine
Is something that ought to be seen;
I perform some high jinks:
With the knots and the links;
I hope that you see what I mean!
Renzo Ricca, University College, UK
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.
Zbigniew Peradzy'nski, Warsaw, Poland
My passion for diff'rential forms
Defies all traditional norms;
It may make you queasy,
But it's really quite easy;
It ought to be taught in the dorms.
Carlo Barenghi, Newcastle, UK
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.
Tomasz Lipniacki, Warsaw, Poland
Research on fields anisotropic
Is surely an interesting topic;
The unit binormal
Shows features abnormal,
As seen if you're not too myopic!
Norman Zabusky, Rutgers, USA
I use methods visiometric,
And I tell you, this is my pet trick;
If in my pot-boiler
Compressible Euler
Gives a vortex, then I will project it.
Javier Jimenez, Madrid, Spain
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.
Kai Schneider, Marseille, France
Of wavelets I'm an adherent;
Though some people think me quite errant,
Like the structures extracted
By techniques compacted,
My lecture's entirely coherent.
Tony Leonard, Caltech, USA
I follow a vortical blob
Through stretching and turning and throb;
I can go very far
With pancake or cigar;
You'll see it's a very fine job!
Konrad Bajer, Warsaw, Poland
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.
Peter Constantin, Chicago, USA
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!
John Gibbon, Imperial College, UK
I consider the problem of blow-up,
The vortices rapidly grow up;
They flourish like petals
On flowers among nettles;
You can purchase them down at the Co-op.
Amitawa Bhattacharjee, Iowa, USA
On the singular blow-up of Euler,
I am an inveterate toiler;
I look near the null,
You may think this is dull,
But there's no need to be such a spoiler!
Stephen Cowley S.J., Cambridge, UK
I live in the boundary layer
Which I handle with exquisite care;
When near separation
There's an odd indication
Of something that oughtn't be there!
Rich Pelz, Rutgers, USA
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!
Vlasdislav Zheligovsky, Moscow, Russia
Vortex line transport we follow
For Euler where we like to wallow;
Two grids are employed,
The traps to avoid,
And pancakes emerge; hard to swallow?
Uriel Frisch, Nice, France
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.
Viktor Ruban, Moscow, Russia
We consider the fate of string links,
That can tangle with all sorts of kinks;
I won't try to disguise
What we regularise;
It's more subtle than anyone thinks!
Andrei Muravnick, Moscow, Russia
I study a problem of Cauchy;
My methods are not wishy-washy;
My theorem three
Is contrarily
An achievement that's `ochen kharoshi'.
Constantin Pankrashkin, Moscow, Russia
I'll paint you a dazzling picture
Of the truth of the Maslov conjecture;
Self-similarity,
Weak singularity --
That is the gist of my lecture.
Marie Farge, Paris, France
I use without any compunction
A well-chosen wavelet function;
With theorems nice,
And methods concise,
My results are immune to debunction.
Bogdan Cichocki, Warsaw, Poland
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.
Maria Ekiel-Jezewska, Warsaw, Poland
When spheres are tending to impact,
The question is: do they make contact?
When stick turns to slip,
The forces can dip;
And this is the tough nut that I've cracked.
Cezary Sliwa, Warsaw, Poland
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!
Alexander Gourji, Kiev, Ukraine
As three vortices follow their paths
There's a chance for some elegant maths;
There's absolute chaos
From Kiev to Laos,
You may see this in rivers and baths.
Tatsuyiki Nakaki, Kyushu, Japan
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.
Vladimir Malyuga, Kiev, Ukraine
Stokes flow in a trihedral corner,
Of the kind where sat little Jack Horner,
Can be solved without sham
By the method of Lamb;
When I've finished, you won't feel forlorner.
Thomas Gomez, Paris, France
I'll try to put it in words:
You may think I'm away with the birds!
Turb'lence compressible
Gives spectrum of decibel
K to the minus five-thirds.