Converting Navier-Stokes Equations to Lagrangian Frame of Reference

[cahill8]

Homework Statement

I am asked to write down the momentum (navier-stokes equations) equations in the Lagrangian coordinate system. Gravity and viscosity can be ignored.

Homework Equations

[PLAIN]http://img443.imageshack.us/img443/974/65019601.jpg (Eulerian Frame)

The Attempt at a Solution

Am I correct in thinking that I only need to change the RHS to change with time instead of position? The RHS only contains p, so can I split this up into px, py, pz? I can't seem to find any relevant information anywhere.

 

[minger]

No, the fundamental difference between Eulerian and Lagrangian frames of reference (not coordinate systems) is that with Eulerian, the control volume is fixed in space, whereas Lagrangian moves with the flow.

The effect this has on the equations is that you end up with total (also called substantial) derivatives in the Lagrangian frame of reference. You'll end with something like:
<br /> \rho\frac{D\vec{V}}{Dt}<br />
Rather than
<br /> \rho\frac{\partial \vec{V}}{\partial t}<br />

You need to understand what a total derivative is to convert what you have into the Lagrangian form. If you need more help, let me know.