Tuesday, January 13, 2009

Eulerian Ornithology

Nikhil, totally excited: "Macha, you should have been there at Tressider this afty. Babes, babes and more babes everywhere da! The babe density was so high that if you saw a babe at a location, you didn't need to move your eyes to follow her. You could be certain that an equally hot babe would be at the same spot in the next instant!"


When you're analyzing motion of a fluid, you have two approaches. The first, called the Eulerian, is to look at one small region in space and see what happens in time at that region. You'd do this if, say, you were measuring the rate of flow of a river at some place.

The second option is to tag a little drop of fluid and follow the drop as it moves. You could do this by putting a small drop of ink that doesn't mix with the flow, for example. You'd do this if you were interested in designing a wing so that the flow over it is smooth.

One of the first things that made me totally fall in love with Feynman many years ago was this example of his that brought out the difference: Consider a liquid going around with uniform velocity in a circular tube with a circular cross section. At any one point in the tube, the velocity of the fluid would not change in time. But if you followed a single particle of water, it's velocity would change direction constantly!

If I ever teach a class on Fluids, I'll give the babe example before I discuss this topic :-)


N said...

Cap. It. Al!

And lovely title.

Kedar said...

I knew there was some form of science in everything.. But fluid dynamics? That's an eye-opener..

shreevatsa said...

Great example :)

From the title, I was expecting something else. (Specifically, how to traverse all edges, with each exactly once.)

Mahesh Mahadevan said...

By the way, the ink-in-the-water (wish I could say smoke on the water, but hard luck) is Lagrangian - I guess there isn't one day I haven't heard these words from the profs here.
When you relate using Reynolds transport theorem, you do go from Eulerian Ornithology to Lagrangian Ogling.

Ramkumar R. Aiyengar said...

Trouble is this: You follow the babe and miss others passing through that point. You fix your sight at a point and the babe you were ogling at the previous instant isnt in sight. Who else but a software engineer would know better about space-time tradeoffs! :p

Shoban said...

Stud example for Eulerian and Langrangian approach. Thanks to Nikhil, flu-mech will benefit. :D

Space-time tradeoff and Eulerian path on ornithology. Nice.

Vikas Shenoy said...

Bheshh! :-)

In this specific case, I think the Eulerian approach is better as it avoids a heartbreak. In the other case, there is a possibility of the particle (the babe) annihilating due to an anti-particle.

VAV said...

there is also a technique called flow visualization... using photography
i think you should study and show some results to prove the basics of fluid dynamics

Mathew said...

Catherine the Great to Euler. "You are my one eyed cyclops."
He would literally have had to 'eye' her.

Mohan K.V said...

@N: Thank you, kind sir!

@W: :D

@Shreevatsa: Haha, that's a lovely page! Apropos of Euler's pervasive reach, I was trying to calculate my prof's Erdős number recently, and came across this little snippet in WP: "Erdős was one of the most prolific publishers of papers in mathematical history, second only to Leonhard Euler; Erdős published more papers, while Euler published more pages."

@Nai: LOL!

@Dynamic Thalai: Re. real world issues, Pooh, what is the real world but a crude approximation to our equations? :)

@Shoban: Thanks guru, infinitely long time since we spoke! Will buzz you sometime.

@Vikas: A most wise observation, but I take some solace in the fact that is not Chennai :)

@VAV: Why, that would be my greatest pleasure! Hm, now to write up a proposal and find some funding..

Btw, who are you?

@ár Seanchaí! LOL, wicked fellow, this Euler chap.

abhinav narain said...

That is one good post da ... now i can actually love my physics minor by relating this example and many analogies i wud invent :) ( hope not to put in blogs !!

taikun said...

Since I don't work as an engineer nor do I plan to later, being able to enjoy this post seems to be the only benefit so far, of studying fluid mech.