"nomadic life" is correct and usable in written English.
You can use it to describe a life of regular movement, as in "The nomadic life of a traveler often leads to unique and interesting experiences."
I've lived a very nomadic life.
Has he finally given up the rootless, nomadic life, then?
In Finnish Lapland there is some nomadic life based mainly on the reindeer industry.
Today, the rigours of nomadic life are largely a thing of the past.
While living a nomadic life as a young coach with a family, he had few savings.
Patrick's nomadic life gives the book part of its exotic tone.
Meanwhile, he led a nomadic life, holding several brief tutorships at Edinburgh, Dunkeld, and elsewhere.
Their nomadic life was gradually curtailed by the encroachment of settled agriculture on the pasturelands.
"It's been a long time in the making for me, this nomadic life," Mr. Gerstein said.
Andre Agassi, Lleyton Hewitt and Ivan Ljubicic all juggled fatherhood and the nomadic life on tour.
Some young people are abandoning nomadic life for lucrative urban jobs.
