He goes on explaining that "(a dolphin) must have nerves under its skin with extreme sensibility that play the role of manometers which allow him to discover when an eddy is starting to develop. Then, with an appropriate movement of his skin, he neutralizes the recently formed eddies".
Have you ever met Piccard? If you read Tintin adventures, perhaps you've met him. Also, Star Trek fans know his grand-grandson, Jean-Luc.
I don't know if Mr. Piccard was right and if his explanation of dolphin Cd has been superseded, btw.
However, what if there were new mathematical tools that allow you to develop a car, a plane or a submarine that could be "fitted with sensors that will help them adapt to these (Lagrangian) structures"?
So, for those who are not up to date, allow me to introduce what's a Lagrangian coherent structure.
The general idea is this one: there is already a "nice repertory of tools to tackle time-independent and time-periodic systems" for engineers. On the other hand, we've lacked good tools for analyzing time-dependent dynamical systems. As I understand the problem, we depend on numerical solutions to solve these kind of systems, using CFD, for example.
Dynamical systems, generally, follow this couple of vector equations (t being the independent variable, time):
The first equation states that the derivative of one parameter x (position, for example) is equal to another parameter v (speed). The second equation says that the position at time zero is the initial position.
Those of you that studied differential equations know that those equations traces curves from the time t0 to the time t. These curves are called the "flow map".
The flow map is defined as
Now, let's see an example: this is a pendulum to the left of the image and its "manifold" to the right. The blue curve separates the stable movements from the unstable. Here you have the stable movement; the purple dot marks the movement inside the manifold:
If the pendulum moves "over the top", you go into the unstable portion of the manifold, into the red curves region, like this:
Now, time-dependent dynamical systems have those zones of distinct behavior. The lines that divide those zones are called "separatrices" (from the latin word for separate) because particles at different sides of the separatrices will follow different paths. This is a picture of separatrices and the particle paths at each side of them:
Those separatrices are called Lagrangian Coherent Structures. You can use finite time Lyapunov functions to solve them. Here you have an example of a flow over a GLAS-II wing:
GLAS-II wing: an interesting topic in itself, perhaps somebody can explain to me why aren't they used in F1 (I guess they qualify as active aerodynamics, but, hey, we already have active front wings)
Real GLAS-II wing, 1942 vintage: it's not precisely science fiction
Finally, I get to the point: shouldn't CFD packages use these Lagrangian Coherent Structures to define the grid for simulations, instead of small squares? After all, you know they form a kind of impassable border for particles (although these borders fluctuate all the time).
I understand (and I might be wrong) you could use this "natural" grid to enhance the speed of computations. In the end, you could have a skin with sensors, actuators and a computer, so Mr. Piccard dream of an active submarine that imitates a dolphin could become a reality.
Here you have the article that gave me the idea: http://www.nytimes.com/2009/09/29/scien ... ef=science
I apologize in advance for any aerodynamic barbarisms that I could have introduced in my half-digested readings and for the digressions in my redaction.
