multi-layer shallow water or Sigma coordinate?

Hadian

I want to predict the scour hole around bridge piers or bridge abutments using a math. model. In this way I searched the methods, Shallow water modeling can't do that because it dont consider downward and secoundary flows. I think that is better to use multi-layer or layer-integrated shallow water equation or sigma coordinate system to solve this problem, but I could not find any useful paper or text to help me aboute the best choice (which method) and its formulation and numerical schemes.

Regards-Hadian