Dimensions of standing waves at steps in mountain rivers

Oscillations of the water surface are common features of flows around critical conditions (Fr ~ 1) and of both natural and structure-induced undular hydraulic jumps. The paper describes experimental tests and field data on the dimensions of standing waves created by artificial drops in steep gravel bed rivers. The purpose of the research is to analyze what parameters affect the phenomenon, to provide semiempirical formulations for wave dimensions, and to assess whether previous models for undular hydraulic jumps and antidunes are reasonably predictive. The dimensionless wavelength and wave amplitude were correlated to the Froude number at the sill. The first wavelength appears linearly related to the Froude parameter, whereas the amplitude of the first wave shows a less defined behavior, possibly indicating that a maximum value occurs for sill Froude numbers around 1.6-1.7. The corresponding wave steepness (i.e., wave amplitude/length) results between 0.15-0.16, and this range also characterizes the point at which the dimensionless trough depth below the sill achieves a local maximum, probably related to hydrodynamic conditions just before wave breaking. The transition between roller and undular jumps at drops is then argued to likely represent a critical stage in step pool streams, and the hydraulic and morphological implications of this finding are also discussed, with particular emphasis on step stability and step wavelength.