auf … zu…

This probably isn’t worth its own post so I’ll just ask it here (although things never end up being as simple as I envision them). In my lessons I’ve come to the following two sentences:

“Das Auto fährt auf das Tunnel zu.”
” Die Kinder rennen auf das Meer zu.”

I’ve tried to look up what exactly is being conveyed by the auf…zu construction. It almost looks like “into” but I’m used to seeing simply “in” for that. Any help is appreciated.

 

(originally asked by Joe at http://www.german-is-easy.com)