So from his point of view, waiting awhile for something to turn up seems about the best strategy available.

Caught it while we were waiting for you to turn up yesterday morning.

I'm a great believer in waiting for the right thing to turn up.

I was only waiting for him to turn up here.

They'll wait for their two friends to turn up.

Until then, we must wait and watch for something to turn up.

I can't just sit around waiting for something to turn up.

So should I sit around doing nothing, just waiting for something to turn up?

And if it's somebody waiting for me to turn up with the papers, they can think again.