D'Alembert-Euler condition

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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 $\ddot{\mathbf{x}}=\frac{D^2\mathbf{x}}{Dt}$ be the second material derivative of x. Then the d'Alembert-Euler condition is:

$\mathrm{curl}\,\mathbf{x}=\mathbf{0}$ .

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 1700's. It is not to be confused with the Cauchy-Riemann conditions.

References

Truesdell, Clifford A. (1954). The Kinematics of Vorticity. Bloomington, IN: Indiana University Press. See sections 45–48.
d'Alembert–Euler conditions on the Springer Encyclopedia of Mathematics

Category: Fluid mechanics