Is there a special name for along-course elevation profiles of rivers, and where you can you find them? Was discussing the terrain and rivers of Europe today with my father and it became apparent that a graph of the elevation versus course of a river would offer interesting insight, including a quick summary into the elevation of various cities of interest along the course, and some loose feel for the possible speed of the river in various spots.

I did find one image fitting the general theme of what I was looking for regarding the upper Mississippi River at an Army Corp of Engineer's website:



But I didn't have any subsequent luck in Googling the terms used there, nor on any additional terms, for rivers like the Rhine and Danube.

Are these along-course cross-sections made enough that there's a name for them?

And if so, is there any resource where such images can readily be found for major rivers worldwide?
I guess there are multiple names, but I know it as the river's "long profile", and it is used in academic papers (one example here and a search in google scholar here). But you can find similar diagrams under names like the river's height profile, longitudinal profile, longitudinal map or geographic profile. These last two are the ones used in an Australian government web page that have many of those profiles for all major rivers in Australia, with the cities along the river and other information. I'm not aware of a global repository of long profiles.

The following picture is from the same link pointed above (from Geography AS Notes)



A quick search for "Danube long profile" put the following image in the second position of the results



Taken from here