Gravity-capillary waves in countercurrent air/water turbulent flow

Using the Direct Numerical Simulation (DNS) of the Navier-Stokes equations, we analyze the dynamics of the interface between air and water when both phases are driven by opposite pressure gradients (countercurrent configuration). The Reynolds number ($Re$), the Weber number ($We$) and the Froude number ($Fr$) fully describe the physical problem. We examine the problem of the transient growth of interface waves for different combinations of physical parameters. Keeping $Re$ constant and varying $We$ and $Fr$, we show that, in the initial stages of the wave generation process, the amplitude of the interface elevation grows in time as $t^2/5$. Wavenumber spectra, $E(kx)$, of the surface elevation in the capillary range are in good agreement with the prediction of the Wave Turbulence Theory. Finally, the wave-induced modification of the average wind and current velocity profiles is addressed.