What saturates the centrifugal instability?

I sometimes have research ideas that I think are cool, but that don’t make sense for me to pursue. I generally just make a note of them and move on. This is the 24th post in a series describing some of the ideas I’ve accumulated. This idea is based on a paper by Xihui Zhao and Jim Fuller.

What saturates the centrifugal instability?

What’s the idea?

The centrifugal instability is a linear instability (section 4) caused by the centrifugal force. If fluid elements conserve angular momentum the rotation provides a restoring force and there is no instability, but if angular momentum is transported quickly relative to the oscillation frequency then the elements may be displaced at constant angular velocity, resulting in unstable motion.

The idea here is to investigate the non-linear saturation mechanism of this instability in stars.

Why is this important?

The centrifugal instability may be a major driver of mass-loss in rapidly-rotating stars.

How can I get started?

The instability relies on the adiabatic index $\gamma$ staying small. As the instability grows material moves outwards, cools, and I think that increases $\gamma$ (at least in the stars Zhao & Fuller considered). That could be one damping mechanism.

Another possibility is that angular momentum transport gets inefficient as the material approaches escape velocity and effectively decouples from deeper parts of the star. A challenge to this is that angular momentum might be transported by frozen-in magnetic fields, which wouldn’t care about the material becoming less dense.

It could also be that this instability saturates the way most instabilities saturate, namely through non-linear fluid interactions (e.g. $v\cdot\nabla v$). That saturation level also seems worth calculating.