Modeling quiescent phase transport of air bubbles induced by breaking waves

Abstract

Simultaneous modeling of both the acoustic phase and quiescent phase of breaking wave-induced air bubbles involves a large range of length scales from microns to meters and time scales from milliseconds to seconds, and thus is computational unaffordable in a surfzone-scale computational domain. In this study, we use an air bubble entrainment formula in a two-fluid model to predict air bubble evolution in the quiescent phase in a breaking wave event. The breaking wave-induced air bubble entrainment is formulated by connecting the shear production at the air–water interface and the bubble number intensity with a certain bubble size spectra observed in laboratory experiments. A two-fluid model is developed based on the partial differential equations of the gas–liquid mixture phase and the continuum bubble phase, which has multiple size bubble groups representing a polydisperse bubble population. An enhanced 2-DV VOF (Volume of Fluid) model with a k − ϵ turbulence closure is used to model the mixture phase. The bubble phase is governed by the advection–diffusion equations of the gas molar concentration and bubble intensity for groups of bubbles with different sizes. The model is used to simulate air bubble plumes measured in laboratory experiments. Numerical results indicate that, with an appropriate parameter in the air entrainment formula, the model is able to predict the main features of bubbly flows as evidenced by reasonable agreement with measured void fraction. Bubbles larger than an intermediate radius of O(1 mm) make a major contribution to void fraction in the near-crest region. Smaller bubbles tend to penetrate deeper and stay longer in the water column, resulting in significant contribution to the cross-sectional area of the bubble cloud. An underprediction of void fraction is found at the beginning of wave breaking when large air pockets take place. The core region of high void fraction predicted by the model is dislocated due to use of the shear production in the algorithm for initial bubble entrainment. The study demonstrates a potential use of an entrainment formula in simulations of air bubble population in a surfzone-scale domain. It also reveals some difficulties in use of the two-fluid model for predicting large air pockets induced by wave breaking, and suggests that it may be necessary to use a gas–liquid two-phase model as the basic model framework for the mixture phase and to develop an algorithm to allow for transfer of discrete air pockets to the continuum bubble phase. A more theoretically justifiable air entrainment formulation should be developed.