What is Enstrophy & Why Is It Used?

[Ramone]

Hi,

I'm doing some work and keep coming across Enstrophy. Wikipedia gives a description that provides some insight, however I was hoping that someone could explain why its a measure that is used and what does it tell us?

 

[Jolb]

If we had a vector field, take for example a field that denotes the velocity $\vec{v}$ of a fluid at every point throughout the fluid, then the vorticity $\vec{\omega}$ is defined as the curl of the velocity, i.e., $\vec{\omega}:=\nabla\times\vec{v}$. The enstrophy is defined as the mean square of the of the vorticity.

An incompressible fluid can be described entirely by its vorticity field. In other words, we can characterize a fluid's motion entirely by specifying exactly how much it circulates around every point [instead of specifying its velocity at each point]. Enstrophy is a useful concept when we work with vorticity fields: e.g. enstrophy is a conserved quantity when a fluid has no dissipation or external driving forces.

Here's a good reference: http://physics.aps.org/articles/v4/20

 

[Ramone]

Thanks Jolb,

It makes sense in relation to vector fields!

Now I can continue to read this paper.