The Morton number and its importance in free-surface flow modelling

Environmental free-surface flows encompass a wide range of applications in civil and environmental engineering. Hydraulic models, physical and numerical, are developed based upon the fundamental principles of similitude and dimensional analysis, as well as conservation of mass, momentum and energy, to ensure a reliable prediction of full-scale performances. Free-surface flows are modelled using a Froude similitude because gravity effects are important. Practically, the vast majority of free-surface flow models use water and air as in prototype. This constraint implies an invariant Morton number. With a combined Froude and Morton similarity, the Reynolds number is proportional to the mass flux. and it is typically much smaller in the hydraulic model. The difference in Reynolds numbers between model and prototype accounts for potential scale effects in terms of both viscous and capillary processes. It is demonstrated that the Weber number is irrelevant when the Reynolds number is retained. A few hydraulic models used different fluids between models and full-scale applications, and their application is discussed.