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

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