Analysis of antidune migration direction

Antidunes are bed forms characteristic of upper regime unidirectional flows. Contrary to bed forms developed in lower regime flows, antidunes not only can propagate in the downstream direction but can propagate upstream or remain stationary. In this work we analyze the stable hydraulic conditions that determine each of the three antidune movement possibilities, and a new theory is developed for distinguishing the occurrence of each of these conditions. The theory is developed from an energy balance over a symmetrical antidune; for this, the Bernoulli equation is applied between the antidune crest and antidune trough, and the pressure head is corrected to account for the centrifugal forces generated by curvilinear flow. Manipulation of the fundamental equations produces an antidune mobility dimensionless number (F-a), dependent on the Froude number, the mean water depth, and the antidune wavelength. The critical value of the antidune mobility number (F-a = 1) corresponds to the stationary condition, while values higher and lower than the critical correspond to downstream and upstream propagation, respectively. Theory predicts that for a given Froude number, downstream-migrating antidunes are formed for higher water depth-wavelength ratios than for upstream-migrating antidunes. Likewise, by introducing a restriction for the maximum stationary wave height above antidunes, theory predicts that downstream-migrating antidunes could attain steeper height-wavelength ratios than upstream-migrating antidunes. Comparison with published experimental data in literature largely showed agreement between theory and experimental observations.