If a river suddenly changes from a steep slope to a gentle slope, what kind of water surface profile would you expect to see right after the change?

When a river suddenly changes from a steep slope to a gentle slope, the water surface profile immediately after the change would typically exhibit a hydraulic jump. On the steep slope upstream, the water often flows at a high velocity and shallow depth, a condition known as supercritical flow. In supercritical flow, the water moves faster than a wave can propagate upstream, meaning disturbances cannot travel upstream. The Froude number, a dimensionless quantity comparing inertial forces to gravitational forces, is greater than one for supercritical flow. As the river encounters the sudden reduction in slope, the flow naturally tends towards a slower velocity and greater depth, characteristic of subcritical flow, where the Froude number is less than one and disturbances can travel upstream. The transition from supercritical flow to subcritical flow cannot occur smoothly and gradually across the critical depth (the depth at which the Froude number equals one). Instead, this transition is accomplished abruptly through a hydraulic jump. A hydraulic jump is a phenomenon where there is a sudden and turbulent increase in water depth and a corresponding decrease in velocity over a short distance. It appears as a standing wave or a series of turbulent waves. The jump dissipates a significant amount of the water's kinetic energy through turbulence and mixing. Therefore, right after the change in slope, one would observe shallow, fast-moving water (supercritical flow) abruptly changing to deeper, slower-moving, turbulent water (subcritical flow) via this hydraulic jump.