The pattern of surface waves in a shallow free surface flow

• Published in: Journal of geophysical research. Earth surface 2013-09, Vol.118 (3), p.1864-1876
• Main Authors: Horoshenkov, K. V., Nichols, A., Tait, S. J., Maximov, G. A.
• Format: Article
• Language: English
• Subjects: Air-water interface; Capillary waves; Flow characteristics; Flow velocity; Free surfaces; Gravel; Hydraulic roughness; Hydraulics; Reynolds number; River beds; Sedimentary structures; Shallow water; Surface flow; Surface waves; turbulence; Water flow
• ISSN: 2169-9003; 2169-9011
• DOI: 10.1002/jgrf.20117

This work presents new water surface elevation data including evidence of the spatial correlation of water surface waves generated in shallow water flows over a gravel bed without appreciable bed forms. Careful laboratory experiments have shown that these water surface waves are not well‐known gravity or capillary waves but are caused by a different physical phenomenon. In the flow conditions studied, the shear present in shallow flows generates flow structures, which rise and impact on the water‐air interface. It is shown that the spatial correlation function observed for these water surface waves can be approximated by the following analytical expression W(ρ)=e−ρ2/2σw2cos(2πL0−1ρ). The proposed approximation depends on the spatial correlation radius, σw, characteristic spatial period, L0, and spatial lag, ρ. This approximation holds for all the hydraulic conditions examined in this study. It is shown that L0 relates to the depth‐averaged flow velocity and carries information on the shape of the vertical velocity profile and bed roughness. It is also shown that σw is related to the hydraulic roughness and the flow Reynolds number. Key Points Dynamic roughness pattern on water flow surface was studied A model was proposed to describe this pattern mathematically The parameters in this model were related to the hydraulic flow characteristics