Decay of gravity-capillary waves in air/water sheared turbulence

Direct Numerical Simulation (DNS) is used to analyze the wave-decay process in a countercurrent air/water turbulent flow. Three dimensionless numbers describe the problem: the Reynolds number Reτ (which measures the importance of inertia compared to viscosity), the Weber number We (which measures the importance of inertia compared to surface tension) and the Froude number Fr (which measures the importance of inertia compared to gravity). We keep Reτ constant and we vary We and Fr. Regardless of the values of the physical parameters, we observe an initial exponential decay followed by the achievement of a new statistically stationary condition. The parameters characterizing this exponential decay do depend on the specific values of Re, Fr and We. Wavenumber spectra computed at different time instants during the wave decay process reveal that the spectral properties of waves change in time: starting from a condition characterized by the predominance of low-wavenumber waves, we observe a “blue shift” of the energy spectra towards higher wavenumbers, indicating the emergence of a strong capillary behavior. At the new asymptotic steady state condition, wave energy spectra are in fair agreement with the predictions given by the Wave Turbulence Theory. We also characterize the statistical behavior of the interface deformation to highlight the interplay between gravity and surface tension in determining the interface structure.