History and physical significance of the roughness Froude number

ABSTRACT

The roughness Froude number is a relatively new dimensionless parameter that began appearing in the hydraulic engineering literature in the late 1970s, first for the analysis of aeration inception in smooth chutes, and then later in connection with stepped chutes. This article reviews its foundations, historical development, alternative forms, present-day applications, and physical significance, which has received little attention previously. In addition to its empirically demonstrated connection to aeration inception, this paper shows that one form of a roughness Froude number has a strong relation to the transition between nappe and skimming flow regimes of stepped chutes, while another combines the dimensionless flow friction factor and the relative submergence of roughness elements.

Keywords:

• Aerated flow
• aeration inception
• boundary layer
• nappe flow
• roughness Froude number
• skimming flow
• stepped chutes

Acknowledgements

The author greatly appreciates the contributions of the anonymous reviewers and associate editor who made insightful comments that led to significant improvement of the paper, especially the suggested alternate physical interpretation of F_* as a combination of the friction factor and relative submergence of roughness elements.

Disclosure statement

No potential conflict of interest was reported by the author.