2012-20.md

course	course_year	question_number	tags	title	year
Fluid Dynamics	IB	20	IB 2012 Fluid Dynamics	Paper 2, Section I, A	2012

Starting from Euler's equation for the motion of an inviscid fluid, derive the vorticity equation in the form

$$\frac{D \boldsymbol{\omega}}{D t}=\boldsymbol{\omega} \cdot \nabla \boldsymbol{u}$$

Deduce that an initially irrotational flow remains irrotational.

Consider a plane flow that at time $t=0$ is described by the streamfunction

$$\psi=x^{2}+y^{2} .$$

Calculate the vorticity everywhere at times $t>0$.