d'Alembert-Euler condition explained

In mathematics and physics, especially the study of mechanics and fluid dynamics, the d'Alembert-Euler condition is a requirement that the streaklines of a flow are irrotational. Let x = x(X,t) be the coordinates of the point x into which X is carried at time t by a (fluid) flow. Let

\ddot{ x }=\frac be the second material derivative of x. Then the d'Alembert-Euler condition is:curl x = 0 .

The d'Alembert-Euler condition is named for Jean le Rond d'Alembert and Leonhard Euler who independently first described its use in the mid-18th century. It is not to be confused with the Cauchy–Riemann conditions.

References

• Book: Truesdell, Clifford A. . Clifford Truesdell

. Clifford Truesdell . The Kinematics of Vorticity . 1954 . Indiana University Press . Bloomington, IN. See sections 45–48.

• d'Alembert–Euler conditions on the Springer Encyclopedia of Mathematics