This is something I used to feel when I was younger, in my late teens and early 20s, the sensation has not occurred now for many years. I am in my mid-50s.
You describe it very well, a sensation like a wave or subtle movement of my brain within my head, without pain. In my case, the wave-like sensations were most always disjointed, and never lasted longer than a few seconds.
Back then, I also used to get classic migraines preceded by a visual aura or tingling in my lips or fingers. I now tend to get cluster headaches, with no aura. I take medication that works very well to prevent them.
That was years before I was diagnosed with MS, I have no idea if there was a relation.
The doctors I spoke to about the sensation back then never had any idea what it was. One suggested that it might be a very mild form of seizure.
CCSVI Procedure 9/16/2009 at Stanford
Stent in left and right IJVs
Copaxone and Ampyra user
Botox Bladder Injections