Rivermorph software requires quite a bit of river channel and cross section data and having the Rosgen training courses helps bring out its capabilities. They have a short term trial version of Rivermorph available with some examples. I attached the users manual to give you an idea of capability. If the water is clear enough, mapping the channel system with green LiDAR may be helpful in mapping the approximate channel detail. http://freedom.dicea.unifi.it/massimo.rinaldi/RiqFluv%20IAT/RIVERMorph%20manual.pdf
Rivermorph software requires quite a bit of river channel and cross section data and having the Rosgen training courses helps bring out its capabilities. They have a short term trial version of Rivermorph available with some examples. I attached the users manual to give you an idea of capability. If the water is clear enough, mapping the channel system with green LiDAR may be helpful in mapping the approximate channel detail. http://freedom.dicea.unifi.it/massimo.rinaldi/RiqFluv%20IAT/RIVERMorph%20manual.pdf
I would agree with Mr Roland Yonaba, who has given a long list of probable software which can be used for your purpose.
However, I can add a caution. before using any software, you may have to check its capabilities, data requirements, and possible results, result format, etc.
Otherwise, it may happen that your requirement is very simple, and even an analytical solution could have been sufficient.
I am not giving this caution, without such incidences experienced in the past !!
I suggest you to try Telemac-2D model where you can either separately simulate the hydrodynamics or couple with SISYPHE model to simulate the bed evolution. For details, visit (www.opentelemac.org) It is open-source program, you can even play with source code if you need.
Additionally, you can also try IRIC interface which consists of different models within it. This is also a free software but not open-source.
Finally, there is also CCHE2D model. It can simulate the bed change including bank erosion. You can download it but the free version can handle only upto 5000 mesh nodes.