Space-scale-time dynamics of liquid–gas shear flow

Two-point statistical equations of the liquid-phase indicator function are used to appraise the physics of liquid–gas shear flows. The contribution of the different processes in the combined scale/physical space is quantified by means of direct numerical simulations of a temporally liquid–gas shear layer. Light is first shed onto the relationship between two-point statistics of the phase indicator and the geometrical properties of the liquid/gas interface, namely its surface density, mean and Gaussian curvatures. Then, the theory is shown to be adequate for highlighting the preferential direction of liquid transport in either scale or flow position space. A direct cascade process, i.e. from large to small scales, is observed for the total phase indicator field, while the opposite applies for the randomly fluctuating part, suggesting a transfer of ‘energy’ from the mean to the fluctuating component. In the space of positions within the flow, the flux tends to redistribute energy from the centreline to the edge of the shear layer. The influence of the mean shear rate and statistical inhomogeneities on the different scales of the liquid field are revealed.