2006-57.md

course	course_year	question_number	tags	title	year
Fluid Dynamics	IB	57	IB 2006 Fluid Dynamics	1.I.5A	2006

Use the Euler equation for the motion of an inviscid fluid to derive the vorticity equation in the form

$$D \boldsymbol{\omega} / D t=\boldsymbol{\omega} \cdot \nabla \mathbf{u} .$$

Give a physical interpretation of the terms in this equation and deduce that irrotational flows remain irrotational.

In a plane flow the vorticity at time $t=0$ has the uniform value $\boldsymbol{\omega}_{0} \neq \mathbf{0}$. Find the vorticity everywhere at times $t>0$.