Empirical Determination of Free Alternate Bar Length

Abstract

A new empirical equation for free alternate bar length at the fully developed state is introduced. The equation is developed on the basis of dimensional analysis and all readily available data. A special effort is also made to align the formulation with findings from existing theoretical and numerical analyses of the development of alternate bars, and more specifically those resulting from a stability analysis of the phenomenon. When applied to the existing laboratory data, the equation results in significantly less dispersion around the best agreement line than that associated with previous empirical equations, yielding 70% of the data within the 20% error range, against 47% for previous equations. It is shown that previous equations perform notoriously poorly in the case of fully rough subcritical flows and all transitionally rough flows, with the present equation addressing this matter. When applied to field cases, the present equation yielded realistic values of bar length, including for large sand streams with high or very high values of relative depth (e.g., the Tagus and Mississippi Rivers).