Reply to discussion by G. Carosi and H. Chanson on "Turbulence characteristics in skimming flows on stepped spillways"

Abstract

A main technical issue seems to be associated with the structure of the two-phase air–water flow skimming over the pseudo-bottom formed by the step edges. This is a difficult topic. In the air–water skimming flow, the microscopic structure of the gas–liquid mixture is closely linked with the interactions between turbulent vortices and air–water entities (bubbles, droplets, packets) (e.g., Chanson and Toombes 2002; Carosi and Chanson 2008; Gonzalez and Chanson 2008). In the high-velocity free-surface flow, the strong interactions between the turbulent waters and the atmosphere lead to a complete deformation at the interface. Through the free-surface, air is continuously trapped, and the resulting air–water mixture extends through the entire flow (Rao and Kobus 1971; Wood 1991; Chanson 1997). The air–water flow is characterized a complicated two-phase turbulent motion with void fractions ranging from some small, often nonzero values close to the invert to 100% above a pseudo "free-surface" that is usually defined as the location where the void fraction equals 90% (Cain and Wood 1981; Wood 1991; Chanson 1997; Matos 2000). The notion of "effective homogenous flow" contradicts detailed measurements conducted with accurate instrumentations in large-size facilities with well-controlled flow conditions and it is obsolete. Recent findings (Carosi and Chanson 2008) demonstrated in fact a marked changed in flow properties for C ~ 0.95 to 0.97, that is consistent with earlier studies suggesting the use of Y95 or even Y98 as the characteristic air–water flow thickness (Jevdjevich and Levin 1953; Aivazyan 1986)