Bubble entrainment and liquid-bubble interaction under unsteady breaking waves

Derakhti, Morteza
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University of Delaware
Wave breaking is a highly dissipative process, and also a source of turbulence in the ocean surface layer. It entrains a large volume of air in bubbles that rapidly evolves into a distribution of bubble sizes which interacts with liquid turbulence and organized motions. The liquid-bubble interaction, especially in the complex two-phase bubbly ow under breaking waves, is still poorly understood. In the present study, we perform a large-eddy simulation (LES) using a Navier-Stokes solver extended to incorporate entrained bubble populations, using an Eulerian-Eulerian formulation for a polydisperse bubble phase. The volume of uid (VOF) method is used for free surface tracking. We consider an isolated unsteady deep water breaking event imposed by a focussed wave packet. The bubble-induced dissipation and momentum transfer between two phases are considered. The model is shown to predict free surface evolution, mean and turbulent velocities and integral properties of the entrained dispersed bubbles (hereafter bubble plume) fairly well. We investigate bubble plume kinematics and dynamics, turbulence modulation by dispersed bubbles as well as shear- and bubble-induced dissipation, both in spilling and plunging breakers. We nd that the total bubble-induced dissipation accounts for more than 50% of the total dissipation in the breaking region. The averaged dissipation rate per unit length of breaking crest is usually written as b g􀀀1c5, where c is the phase speed of the breaking wave. The breaking parameter, b, has been poorly constrained by experiments and eld measurements. We examine the time dependent evolution of b for both constant-steepness and constant-amplitude wave packets. The scaling law for the averaged breaking parameter is obtained. The exact two-phase transport equation for turbulent kinetic energy (TKE) is compared to the conventional single phase transport equation, and it is found that the former over predicts the total SGS dissipation and turbulence production by mean shear during active breaking. All of the simulations are repeated without the inclusion of dispersed bubble phase, and it is shown that the integrated TKE in the breaking region is damped by the dispersed bubbles about 20% for the large plunging breaker to 50% for the spilling breakers. In the plunging breakers, TKE is damped slightly or even enhanced during the initial stage of active breaking. In addition, we examine the nonlinear interaction of di erent components in a wave packet. Phase locking between spectral components is observed in the breaking region, and explained by calculating the wavelet bispectrum.