Here are the steps to connect a River Mesh Polygon at a fixed culvert level so that the culvert does not have to be full to have inflow from the 2D Mesh.
Step 1. Define the Culvert Type with Fixed losses
Step 2. Define a Mesh Polygon to simulate the River.
Step 3. Define the River Mesh Size
Step 4. At the 2D node defined the elevation interaction between the River Mesh and the Culvert
Step 5. View the Interaction between the River and Culvert.