A degrading way of mocking/comforting someone, in which said person is subjected to excessive stroking of the face, hands, etc. while the Whalefacer says things like 'Shh Shh Shh' and 'Come here. It's OK.'
"For God's Sake! Don't Whaleface me in public! It's embarrassing!"
"I thought you liked me Whalefacing you?"
"At home, yes. In a parking lot? No."