In my experimental tests at the outlet of culverts, I found densimetric Froude number as a very profound parameter to predict the maximum scour depth. This was also confirmed before in the literature as you mentioned.

My experimental tests were conducted under non-cohesive sediment, therefore, I am not sure about the cohesive bed.

About hydraulic jumps, the question is not very clear for me. Are you comparing two different cases with hydraulic jump and without hydraulic jump and observing the changes in densimetric Froude number and also erosion or not.

Because I think after the hydraulic jump there would be a possible energy loss and in any section after that hydraulic jump there is a lower velocity which means you would have a lower densimetric Froude numbers. So let's put it this way, after the hydraulic jump there would be a lower densimetric Froude numbers and may be less erosion. But may its better to confirm it with couple of tests.

Densimetric Froude number is very important parameter for sediment transport and scour rate but there are additional parameters such as electric conductivity in cohesive sediment. If you want to know more information regarding scour in cohesive soil  you can visit websiteof Texas A&M University , you will find open access these related to this topic and professors in civil engineering department  have published a lot of article related to this topic  like  Dr. Jean-Louis Briaud and Dr Kuang-An Chang

Surely, it has an effect on the scour process in two case and should be in considered during the study. 

Ms. Sayana Sorourian: Yes, I was definitely asking regarding effect on densimetric Froude number pre and post-jump. I want to have cognizance of effect of various parameters on the densimetric Froude number. Thanks for your and replies of all others

The densimetric Froude number can be a measure for flow velocity and bed shear stress in the case of density currents f.i. a highly sediment laden flow under clean ambient water. Therefore it is also important to define erosion or sedimentation of the sea- or river bed.

The densimetric Froude number also defines the mode of the flow: super- or subcritical. In the first case only, submerged hydraulic jumps can develop, generating turbulence with local scour and reduction of velocity and bed shear stress successively, that may result in local sedimentation and possibly accelerating again (cyclic steps). We observed these processes in tests with sand-water mixture flows under water.

Publications:

Hyperconcentrated Sand-Water Mixture Flows Over a Flat Bed

A comparative study of sediment waves and cyclic steps based on geometries, internal structures and numerical modeling

On the construction of sand fill dams- Part 1 Hydraulic aspects

For non-cohesive sediments the densimetric Fr number is an important parameter, and maximum scour depth should be correlated to it.

However if cohesion is important, other parameters (involving the cohesion!) have to be considered and then the densimetric Froude number could be less important.