Wayne P. Tanner looked gloomily over the rim of his coffee cup at the row of snow-crusted trucks parked outside the diner. He hated the snow, but more than that, he hated being caught out. And in the space of just a few hours, it had happened twice. Those New York State troopers had enjoyed every minute of it. Smug Yankee bastards. He had seen them slide up behind him and hang there on his tail for a couple of miles, knowing damn well he had seen them and enjoying it. Then the lights coming on telling him to pull over and the smartass, no more than a kid, swaggering up alongside of his innie's step and like some goddamn movie cop.
This is from The Horse Whisperer by Nicholas Evans.
What does slide up mean here? I have seen dictionary definitions, but slide means there to move smoothly over a surface while in contact with it. One meaning says to decrease in amount or value.