[paulzhang]

Is there anyone know how to transform the N-S equation, which is steady in (x,y) coordinates to time dependent in (Epsliong, Etta) coordinates.
Maybe that is a transform from Euler to Lagrange. But I do not know how.
Any idea will be greatly appreciated. I thought about it for quite a long time.

[Shenren_CN]

The basic idea is simply coordinate transformation (or, should I say, chain rule). If you have never done it before, it's very tricky to get every term right.

Most textbooks give you results on orthogonal curvilinear coordinates, which should be enough if your coordinate system is orthogonal. Otherwise, you'll need a more general result, you may need to derive them by hand, a good starting point is the wikipedia link on curvilinear coordinates.

http://en.wikipedia.org/wiki/Curvilinear_coordinates

Originally Posted by paulzhang

Is there anyone know how to transform the N-S equation, which is steady in (x,y) coordinates to time dependent in (Epsliong, Etta) coordinates.
Maybe that is a transform from Euler to Lagrange. But I do not know how.
Any idea will be greatly appreciated. I thought about it for quite a long time.