If you are studying the scour downstream of a hydraulic structure or bridge pier, the maximum scour depth is the most important parameter. The maximum scour depth is not necessarily observed at the end of the experiment. If you continue an experiment for a long time (for example 24 hours) and measure the time development of the scour profile, you can see when the scour reaches equilibrium conditions. I think when the scouring reaches equilibrium, the maximum scour depth is achieved.
Maybe this might be helpful or at least interesting. It’s been a number of years since I read it. https://pubs.usgs.gov/sir/2016/5121/sir20165121.pdf
The maximum stream power and scour depth in structures is likely achieved during annual to severe, episodic hydrologic events of bankfull flow or greater. In streams with high sediment loading, locally scour can occur and then redeposit. Chains imbedded at marked points in rivers are sometimes used to document extent of degradation and deposit during routine annual bankfull to severe events. Stream type can also be a determinant of the potential for increased scour severity. The clean water effect below dams can also increase scour, degradation and losses to point bars.
I don’t know if the Rivermorph software might help if you have ample channel dimensions and flow data. They probably still have a trial version to look at before considering purchase. Dave Rosgen and others have publications addressing measures such as cross vanes and Jhooks to mitigate channel and bank scour.
Sometime when I get back to my computer storage, I have a number of internet search publications that discuss various aspects of stream or channel scour, primary and secondary velocity vectors, flume experiments, etc. Its an interesting subject. And streams are dynamic, with adjustments due to floods, sediment, woody debris, channel structures, instream modifications, etc.