Length scales and the energy balance for turbulence near a free surface

The structure of turbulence near a free surface is examined by using results obtained from a direct simulation of flow between a no-slip wall and a shear free boundary, which serves as a model of a waveless free surface. An energy balance analysis shows that the pressure-strain term is the dominant producing term for the spanwise component of the turbulent kinetic energy. In addition, the dissipation rates for the horizontal components of the turbulence are reduced near the free surface, whereas the dissipation rate for the vertical component remains approximately constant. Two-point correlations, energy spectra, and length scales reveal important free surface induced effects. The length scales near the free surface are compared with the scales near the centerline of normal turbulent channel flow. This comparison reveals an increase by a factor of three in the streamwise length scales associated with the spanwise velocity fluctuations and an increase by a factor of two in the spanwise length scales for the streamwise velocity fluctuations. The length scales normal to the free surface are decreased for all velocity components. This indicates a more pancake-like eddy structure near the free surface compared with the structure near the centerline of a normal channel. The energy spectra show qualitative agreement with the Hunt-Graham model, though higher resolution calculations will be required to make more quantitative comparisons. The streaky structure in free surface bounded turbulent channel flow is noticeably more persistent than in normal turbulent channel flow. This is principally due to the attachment of streamwise oriented wall eddies to the free surface.