d'Alembert–Euler condition

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

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

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.

• Fluid mechanics
• Mechanical engineering
• Vector calculus
• Mathematics stubs

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