Those asking why you can’t just throw a stick or mannequin in river
Here is an extensive military document talking about modelling river systems
It’s dozens of pages, unbearably complicated, and in summary depends on momentum, wind, temperature, rainfall, the random nature of water (ever watched a water droplet make its way down a window?), bedrock, debris, and an obscene amount of maths and equations. Seems simulations have to run for weeks at a time to get anything accurate and that’s not even tidal!
https://www.hec.usace.army.mil/confluence/prospect/files/96241317/99552223/2/1652040714363/1.3+River+Mechanics+and+Intro+to+Unsteady+Flow+Equations+(Jensen).pdf