Integrate the Euler pdes (2.9)

\[ \begin{gathered} \frac{\partial v_{\alpha}}{\partial x_{\alpha}}=0 \\ \frac{\partial v_{\alpha}}{\partial t}+v_{\beta} \frac{\partial v_{\alpha}}{\partial x_{\beta}}=-\frac{\partial p}{\partial x_{\alpha}} \end{gathered} \]

governing the motion of an incompressible, inviscid fluid, along a pathline (Weber's equation).

2.6.1 Write the Euler pdes in mixed spatial/material description.

2.6.2 Transform to strictly material form.

2.6.3 Reformulate the momentum balance using (2.94) such that integration along a pathline starting at \(\mathbf{X}\) becomes possible.

pde (2.9)

Eq (2.94)

Transcribed Image Text:

0, + t 1 + Fr