Impact of turbulence and secondary flow on the water surface in partially filled pipes

Large eddy simulations (LESs) of turbulent flow in partially filled pipes at various filling degrees are conducted to investigate the response of the water surface to the turbulence and the secondary flow below it. LESs are validated first using experimental and direct numerical simulation data. At increasing water depth, the magnitude of water surface fluctuations increases with increasing strength of the main secondary flow. Visualizations of the instantaneous water surface and the turbulent flow underneath reveal that thin surface waves are generated by flow meandering in the shallower case, whereas surface waves in the deeper cases are influenced by the vertical velocity fluctuation. Pre-multiplied spectra of the water surface fluctuation, h′, provide further evidence of the origin of the surface waves. In the shallow flow, the peak frequency of the h′ spectra is consistent with the peak frequency of the u′ and v′ spectra, while for deeper flows, it agrees more with the w′ spectra. Furthermore, the transport patterns of the surface waves are investigated by the wavenumber-frequency spectra. Three types of surface waves are observed in the wavenumber-frequency spectra, i.e., (1) convective waves with phase velocity equaling the surface velocity, (2) irrotational dispersive gravity-capillary waves, and (3) stationary waves caused by secondary currents.