Sorry, I wasn't clear. The idea is that the river was flowing normally on the surface stratum of soil, which it slowly eroded, so that at one point, where the bedrock is closer to the surface for any reason, the bedrock gets exposed. I'm not trying to have a river flowing uphill or something.
Besides, scrap the bedrock, if a river course is narrowed by one or more islands at a certain loin, should not it become more turbulent anyway?