Surface turbulence in film flow over periodic ripples

Turbulence in gravity-driven film flow is usually discussed in terms of three-dimensional solitary-wave pulses as they are frequently observed in flows along smooth walls. Here, we show that free-surface turbulence arises in films along rippled substrates, as they are commonly employed in process engineering applications, already at rather low Reynolds numbers from the irregular break-up of the solitary-wave fronts. Short waves in the capillary regime replace the broken solitary waves beyond a certain Reynolds number. The crossover coincides with the occurrence of steady three-dimensional surface patterns upstream, which suppress travelling waves. The waves show power spectral densities with power-law exponents typical for weak capillary-wave turbulence. With increasing Reynolds number, the steepness of the power law declines to lower levels.