Antidunes are formed in alluvial channels where the Froude number is close to 1. The antidunes are charachterized as waves where the surface wave are in phase with the bed. The most stable antidunes are the downstream-migrating type, which occurs when the Froude number is slightly below 1.
The following two articles have been made on this topic:
Olsen, N. R. B. (2017) Numerical modelling of downstream-migrating antidunes, Earth Surface Processes and Landforms. Vol 42, pp 2393–2401. doi:10.1002/esp.4193.
Olsen, N. R. B. (2016), Numerical modelling of antidune formation and propagation, International Symposium on River Sedimentation, Stuttgart, Germany.
Longitudinal profile of a section of the grid.
Longitudinal section of the flume showing two wavelengths with grid. The colours shows the water velocity.
Longitudinal section showing the pressure field with colours over two dunes.
Video of longitudinal profile - whole flume Note the vertical/horizontal scale is distorted.