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Euler’s Equations
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Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity). They describe the conservation of momentum. We can derive from it the equation for the evolution of vorticity (Helmholtz equation). Euler’s equations have to be supplemented by the conservation of mass and by an equation of state (which relates density to pressure). Of special interest is the case of incompressible flow; when the fluid velocity is small compared to the speed of sound, the density may be treated as a constant. In this limit, Euler’s equations have scale invariance in addition to rotation and translation invariance. d’Alembert’s paradox points out the limitation of Euler’s equation: friction cannot be ignored near the boundary, nomatter how small the viscosity.
Title: Euler’s Equations
Description:
Euler derived the fundamental equations of an ideal fluid, that is, in the absence of friction (viscosity).
They describe the conservation of momentum.
We can derive from it the equation for the evolution of vorticity (Helmholtz equation).
Euler’s equations have to be supplemented by the conservation of mass and by an equation of state (which relates density to pressure).
Of special interest is the case of incompressible flow; when the fluid velocity is small compared to the speed of sound, the density may be treated as a constant.
In this limit, Euler’s equations have scale invariance in addition to rotation and translation invariance.
d’Alembert’s paradox points out the limitation of Euler’s equation: friction cannot be ignored near the boundary, nomatter how small the viscosity.
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