Arnold Schwarzenegger's son hit the beach Wednesday in L.A. with some friends and his smokeshow of a GF ... model Savannah Wix. They took a dip in the ocean, laid on the sand and soaked up some rays. Joseph and Savannah have been dating for at least a year. They seem to be pretty crazy about each other ... the proof's on his Instagram. He shows her off in a bunch of his posts, and ya can't blame the kid.

And while Joseph was in the ocean, Arnold was shaming us all ... hitting up a nearby Gold's Gym with Hugh Jackman. Arnold continues to be the picture of health. Just 3 months ago, he underwent emergency open-heart surgery for a catheter valve replacement.