Numerical investigation of shear-flow free-surface turbulence and air entrainment at large Froude and Weber numbers. (7th October 2019) - Yu, Xiangming; Hendrickson, Kelli; Campbell, Bryce K.; Yue, Dick K. P.
Abstract : We investigate two-phase free-surface turbulence (FST) associated with an underlying shear flow under the condition of strong turbulence (SFST) characterized by large Froude ( Fr ) and Weber ( We ) numbers. We perform direct numerical simulations of three-dimensional viscous flows with air and water phases. In contrast to weak FST (WFST) with small free-surface distortions and anisotropic underlying turbulence with distinct inner/outer surface layers, we find SFST to be characterized by large surface deformation and breaking accompanied by substantial air entrainment. The interface inner/outer surface layers disappear under SFST, resulting in nearly isotropic turbulence with k^-5/3 scaling of turbulence kinetic energy near the interface (where k is wavenumber). The SFST air entrainment is observed to occur over a range of scales following a power law of slope -10/3 . We derive this using a simple energy argument. The bubble size spectrum in the volume follows this power law (and slope) initially, but deviates from this in time due to a combination of ongoing broad-scale entrainment and bubble fragmentation by turbulence. For varying Fr and We, we find that air entrainment is suppressed below critical values Fr_cr and We_cr . When Fr^2>Fr_cr^2 and We>We_cr, the entrainment rate scales as Fr^2 when gravity dominates surface tension in the bubble formation process, while the entrainment rate scales linearly with We when surface tension dominates.