2001-46.md

course	course_year	question_number	tags	title	year
Fluid Dynamics	IB	46	IB 2001 Fluid Dynamics	4.I.7G	2001

Starting from the Euler equation, derive the vorticity equation for the motion of an inviscid incompressible fluid under a conservative body force, and give a physical interpretation of each term in the equation. Deduce that in a flow field of the form $\mathbf{u}=(u(x, y, t), v(x, y, t), 0)$ the vorticity of a material particle is conserved.

Find the vorticity for such a flow in terms of the stream function $\psi$. Deduce that if the flow is steady, there must be a function $f$ such that

$$\nabla^{2} \psi=f(\psi)$$