On the Influence of Microbubbles on the Turbulence Induced by a Surface Wave

We use the direct numerical simulation (DNS) method to study the vortex structure of the near-surface water layer, which is saturated with air bubbles, in the presence of a stationary surface wave. A wave with a wavelength of 15 cm and a steepness of 0.2 (an amplitude of about 0.5 cm) and bubbles 400 μm in diameter (microbubbles) are considered. Complete three-dimensional fluid motion equations (Navier–Stokes equations) are solved by the DNS method simultaneously with the equations of motion of individual bubbles with allowance for their influence on the carrier flow. Under the influence of the surface wave, the flow in the near-surface layer becomes turbulent and characterized by the presence of vortex structures stretched along the wave propagation direction. To analyze the vortex structure of the flow, the instantaneous velocity gradient tensor is calculated, and its complex eigenvalues, whose imaginary part characterizes the local vorticity of the flow, are calculated, while filtering out the contribution of the purely shear component (vortex sheet). Average profiles of the eigenvalues and the fluctuations, which are obtained at the stage of the statistically stationary flow, show that the influence of the bubbles lead to intensification of small-scale vortices and turbulent pulsations in water.