Inverse energy cascade structure of turbulence in a bubbly flow (Numerical analysis using Eulerian-Lagrangian model equations)

The inverse energy cascade in bubbly flow is investigated by a numerical simulation using the Eulerian-Lagrangian model in which the governing equations are formulated with emphasis on the translational motion of bubbles in nonuniform flow. In this paper we are concerned with the validation of the numerical model and various parametric dependencies on the inverse cascade. The calculated results reveal that, 1) continuous growth of the spatial fluctuation scale in a bubble-induced flour is well predicted by the present numerical model and the results have a good analogy with the experimental results which were introduced in our first report, 2) the strong relationship between energy-decaying process and bubble-bubble distance interval is also identified by the present analysis, and 3) the slope of energy-decaying in the high wavenumber region depends on the kinematic viscosity of liquid, and that in the low wavenumber region depends on inhomogeneous buoyancy distribution which changes due to the bubble motion.